I'd like to lay 5/8 inch eng hardwood over concrete subfloor in living room. Problem is the adjacent dining/kitchen area, which has old red oak hardwood which we plan to keep. The living room was added on and there's a 3/8 inch height difference already between the concrete and red oak. So there'd be at least a 1inch difference between the two rooms if I went with the 5/8 eng wood. Is this too much of a step up and will it look bad even with a custom milled transition? Any suggestions? I guess we could look for a thinner eng floor but I hear that the quality ones only go with 5/8 minimum (and I like the product made by oak and broad). All advice appreciated!

Instead of a step up how about a ramping transition....15 degrees.

Even with a ramp is a 1 inch difference still weird/unusual? I assumed a ramp can be milled but wanted to know if this was not recommended above a certain difference in height.

Depending on the layout of the flooring in the room it may be possible to create a ramp type by shimming with layers of roll roofing. It has become expensive recently, but each layer raises the height by one eighth of an inch, with rolls three feet wide.
You may end up covering the whole room with layers gradually thicker near the red oak floor. It will lay flatter if you roll it out then turn it over.
The floating floor will lay over the tar paper with no problem if you can step it every 3 feet.
One inch ramp is a tripping hazard, so maybe a different color of finish on the ramp would help keep it safer.