I don't have a picture (I can grab get one if you like), but I did the same thing in my current project - new wood floor in the kitchen going right into existing in the dining room. The floor installer feathered some of the new boards into the dining room floor so it looked continuous, then I had all the existing floors sanded and refinished and stained the old+new 1 color. The result is a transition that looks completely continuous and uniform. Of course I had to refinish all my existing floors to do it. If you don't want to do that the only thing I can imagine working is a perpendicular strip to edge the new and old. It'd be impossible to match the old stain with new perfectly so you'd need something to separate the two. I have a spot in my house where the boards are mismatched so whomever installed it back in the day put a strip. I attached a picture of that.

I had the same problem. Had old strip flooring that was over 100 yrs old. At one point someone replaced a section with 3/4 thick wood floor but you wouldnt know until it was tore up. When I laid all the flooring an got to the the hallway I was up about 1/2 in. I shimmed up an 1/8 in then stripped a blank of the new floor on the table saw to build a thin transition piece. There is a slight raise but everything is the same level and looks nice. So in short just use a reducer.

Angle at outside of living room to dining room Looking from entry to dining room, kitchen partial wall to left, hallway goes off to the right. The hardwood will go in the kitchen too, the flooring laying around is just that, trying to decide how to run it, and excuse the mess! Fireplace wall not perpendicular to wall hutch is on Entry, kitchen, dining room on left, living room on right. Pictures have the 5400 lbs of white oak in "wheatfield" flooring that came today, acclimating. My eclectic taste, have a new dark leather chesterfield coming as well as three bookcases for along dining room wall to make it more a "library", Have more American Empire Revival furniture including a library table and round pedestal table at another house to bring in once I get the floors done. Creek runs below deck beyond the drapes. Help!

Laying the new floor in the same direction as the old floor is not the normal way to go about this. In the building industry, it is more common to see layers that are staggered or "bricked". In other words if layer #1 is laid in a North-South direction, then layer #2 (the top layer) is laid perpendicular to it in an East-West presentation. If you want to run the new flooring in the same direction as the old, you will want to use some underlayment (plywood) over top of the old floor so that you can maintain the "staggered" or "bricked" layering system. That is one way to maintain the North-South presentation. Please work with hardwood flooring professionals who have some experience renovating these old gems. They will have seen what worked....and what didn't. Their experience will be invaluable on a project like yours.