Another question if someone may dare to help.
I need to go from 3/4" hardwood to linoleum with a flush reducer. I'm looking to try to get one with an overhang because that would make more sense to me but don't know if that is an option.
The flooring will be perpendicular to the reducer.
The flush reducer has a groove so do i just lock in the tongue on the end of the board into the groove of the reducer and nail down the reducer? That doesn't make much sense for expansion gap though. I guess I could run some glue in the groove of the reducer and lock it into the end of the flooring and not nail it to let it float but I would think that it would break free sooner or later.

The run of the reducer from room to room is about 5 ft.

I could put down the reducer then gab between the reducer and the hard wood enough to put in a t molding transition but I think that might look funny.

https://shawfloors.com/flooring/how-to/ ... d-moldings

The thickness of the linoleum is usually an eighth inch. If you have a table saw, you could take an eighth inch off the underside of the reducer where it covers the linoleum, no more than 3/8ths inch, so it still will be the correct height. Since most reducers 3/4 inch thick have channels on the bottom you don't want to cut too deep. Glueing should be fine to keep it in place. If the hardwood has been sanded it may be a little under 3/4 so you would be smart to ease the edge of the new reducer so it will not be a sharp edge. Rounding it over with 80 grit or 100 grit sandpaper will help, if you hav e a little finish to make a touch-up and prevent a splinter. The edge of a new reducer may be close to an eighth inch so you may have a sharp edge there, too, so it could be sharp. Glue there will sometimes prevent a splinter, later.

What is the height difference between the hardwood flooring and the linoleum?

don't know the height difference yet. carpet still in. Wife wants to wait until after x-mas for me to start demo.
Just trying to anticipate problems and figure out solutions first.

I do know there are two layers of linoleum due to pulling the dishwasher lately and seeing the old layer under there.

Depending on the height difference (assuming the top of linoleum is lower than top of new hardwood) you might be able to use a piece of flooring instead of a store-bought reducer. The edge of your homemade reducer would abut the ends of the flooring that runs parallel to it. It would probably be best to install the reducer first. The end grooves of the flooring can go over the reducer's tongue or vice versa. The reducer can be face nailed into the subflooring. Don't worry about an expansion gap....if the reducer wants to expand it would do so in the direction of the linoleum. Lengthwise expansion of the perpendicular flooring is negligible. Undercut the bottom surface of the reducer so that it covers the edge of the linoleum. Also, cut a 15 degree chamfer on the top surface of the reducer to create a 'ramp' onto the linoleum. The thinnest part of the ramp that rests on the linoleum should be approximately 1/4".