My first question is on "if I want to leave an expansion gap"... I was under the impression that this was really need to be done.

In terms of the idea you suggested the top strip (which is at 1.5") is narrower than the rest. But overall I'm not sure if I fully understand what you are meaning. Are you suggesting to basically make a base shoe out of my flooring by slicing a strip off?

I guess I can note that the flooring I pulled up from the hall was butting up against the door frame. I had hardwoods (the acacia) installed in my living room and it is also butted up to the patio door frame.

There is no need to provide any expansion gap at the ends of oak flooring. Even if it gets wet it will not expand lengthwise. If the flooring does get wet you may get buckling, but not from the ends of the boards expanding. It is safe to butt the flooring to the threshold. If you can not make accurate cuts, then you can cover the gaps with shoe. If there is a big difference between the finish flooring height and the top of the threshold you should have some protection for the exposed threshold edge so it will not get splintered or worn excessively by foot traffic.

Wood expands widthwise. Lengthwise expansion is so minimal, at best, that no expansion gap is required to accommodate lengthwise expansion. An expansion gap to accommodate widthwise wood expansion is recommended. As you have seen some installers don't always provide this expansion gap, but IF (big IF) there is extreme expansion the expanding flooring could damage whatever it is butted tight to.
Based on the height measurements, if you install the new flooring it's height will be 3/4" below the height of the threshold. A piece of the flooring on top of the installed flooring would have it's height level with the threshold. So install the new flooring and leave an expansion gap. Place a piece of flooring (transition) on top of the last piece of flooring....butt this transition piece to the threshold....it will cover the expansion gap. A bevel on the transition piece will 'ramp' it down onto the flooring. You can add a thin strip of flooring in the expansion gap to support the edge of the transition piece.

Since the shrinkage between wet and dry wood is generally about a tenth of an inch per hundred inches in length. I guess it could expand a tiny bit. A quarter inch would take care of wet flooring, but the floor would over stress the fasteners and start to buckle up if it got close to 50 % moisture content. Covering a quarter inch gap with a piece of base shoe will look like the base shoe is part of the threshold instead of having a ramp, which will generally project into the room from the slope of one-eighth inch to three quarters inch. A small piece of molding will have a better look while still protecting the threshold from foot traffic.

So as it turns out I had bought both a T-molding and a Reducer from from the flooring manufacturer to cover a couple of different transitions I need to make. For moment I thought I might just just use the reducer as I think it meets your intent. I put it down a moment ago and I think the only real concern might be that the rubber gasket under the door drags on the reducer and even snags on it. If I have it in place and then close the door to it I might be ok, but it will still drag and I imagine wear through the finish on it. I'm not sure if I trust that I can thin down the reducer without damaging it. I'll play with it a bit more but if I can't get it to work I'll plan on a small gap and put the shoe in and be done.

Thank you both for your input.

Now on on to figuring out my next hurdle.

So while I'm at it... at the other end of the hall for this area I am transitioning to tile. The height of the tile off the sub floor is about 15/16". The flooring is just under 3/4". So I could install the T-molding I have at an angle, but that might look a little funny and I'm not sure if it would compromise the strength of it... I could attempt to use the table saw to rip a 1/4" strip off of a piece of flooring and shim it under the t molding on the hardwood side. Hopefully that strip wouldn't get too damaged in the process.. And then I assume I construction glue it all together when I'm done.

The wood flooring is 3/16" higher than the tile? The T-molding won't look right if installed on an angle. To have it sit right you would have to remove 3/16" from the underside of the T-molding on the side that rests on the wood flooring. But the T-molding is too thin to do this. You could build up the bottom edge of the T-molding where it rests on the tile but this may create a toe stubber when walking from the tile floor to the wood floor. Do you have the tools to make your own T-molding from a piece of your flooring material? Also, when you install T-molding face nail it through the T into the sub-floor.

I would make a header board across the doorway. The edge next to the tile could be shimmed up with a layer of tarpaper. The header would have either the tongue or the groove side cut off so the flooring would be T&G where it meets the header.
Be sure to ease the edge of the header next to the tile so it is not sharp, either before you install it with a black plane or sand paper, or you will need to use a chisel after installation. The header should be a little higher than the tile edge so it will protect the tile from things dropping where the tile has been cut which is more susceptible to chipping. Leave a half grout width between the tile and the header that can be caulked with a sanded caulking to match the grout color. I don't like T moldings, but they are need for a floating floor.

That might be an idea. The people who installed he acacia in the other room did something similar when they mated to the same tile.

For here, I was going to run the boards parallel to this threshold to align with the joists. So I could just have the last board raise up on one side theoretically. Measuring, the last board should be about a full plank width, and they are 5" planks.

I had it backward...the tile height is greater than the wood flooring. So cut a 3/16" rabbet on the underside of a piece of flooring. The rabbeted side will rest on the tile and the non-rabbeted side will rest on the wood flooring. Bevel both edges to 15 degrees to ramp down on both sides. Nail this piece to the subfloor. You can leave an expansion gap which this transition will span. This will cover the edge of the tile and give a clean look. This piece can be as wide or narrow as you want.

I could try that. With this idea are you assuming I am using un-finished flooring? What I have is pre-finished. I have a stain which I'm using for base boards which is pretty close, but I'm not sure if I can match it entirely. I could give it a try.

I suppose another option is I install the T I have and add a quarter round at the side I built up to ease the to stubber issue. Or I can try to rip out a bevel cut from the flooring to make the same effect.

A good paint store should be able to make a stain that will match. If you want to use the T molding you have you could add a 3/16" strip to the underside of the edge that will rest on the wood floor. Making your own transition from a piece of flooring with the rabbet would just give you more flexibility with the width....this might be important as you approach the tile with the last piece of flooring e.g. you might have to cut the last piece to a narrow strip to fit.

If you do end up staining some flooring pieces check with the manufacturer for info concerning color and poly.

If your tile is cut straight using a factory pre-finished plank ripped to fill the gap across the tiled doorway with shim under it to get even or a little higher than the tile on the edge of the last board, then ease the edge and use your stain to seal it.
Sanded caulking will make it look great and be "smooth" going through the doorway. Anything that is not close to flat will be wearing as you walk over it and start to look dirty when it gets worn.
You can always shim out past the door jambs with a layer of tarpaper, to make a gradual transition.

I was thinking yesterday that as a first pass I will try taking some extra nosing that I have and see if I can make a transition out of that. The side which has the groove I will notch out (or put in a rabbet) to fit over the edge of the tile. I will reduce the thickness of the entire piece so the rest can sit on the wood floor. I might need to make a brace that runs in the middle so the middle, in the gap between the two floors can rest on the subfloor.