I removed the carpeting in my bedroom to find that the room was originally 2 rooms and that a wall had been removed near the middle of the room. Each half of the room has 3/4" x 2 1/4" existing red oak flooring with a gap in the middle where the wall was. My plan was to remove a 30" wide strip of flooring in the middle of the room and install new flooring as per the sketch below. I had planned to cut a groove in the existing flooring and install a strip to tie the old into the new. After cutting the existing flooring (and hitting several nails) it is apparent that this won't work due to the nails.

I am looking for suggestions for making this joint. I could put in a shiplap joint (cutting above the nails) but am not sure how much help this would be. I would like to avoid surface nailing. Perhaps there is an adhesive that can be used in this situation? Any advice would be appreciated.

Have you cut the 30" swath? Are the nails you are referring to exposed? If so why can't you pull them or cut them off at subfloor level or drive them below the surface of the subfloor?

Yes I have cut the 30" swath.

The existing nails I am referring to are nailed through the tongue (ie. not exposed) in the existing hardwood installation. They used what looks like a hardened steel "cut nail" and are nailed somewhat randomly throughout the floor into the subfloor.

Since you have cut back some of the old flooring you may have noticed that the nailing schedule probably doesn't meet todays nailing requirements of within 3 inches of the butt-joints and every 10-12 inches, for your flooring.
It would be a good idea to fasten all the butt-joints down with new fasteners, since you can't easily know how far from the ends there is a fastener now.
Using a carbide tipped grooving tool so you can have a mechanical joint between the old and new is overrated, in my opinion, if you glue the new flooring to a good sub-floor. You will b e able to have glue push under the old flooring when you spread the glue, so this will be enough to hold the joint in alignment where they meet.
This is a novel way to join the two rooms. Even if you would like to join the rooms together by weaving the flooring together, the boards don't always align across the whole room, so it becomes impossible to get a connection unless all of one of the rooms' flooring is removed and then staggered back for a weave-in.

They are probably flooring cleats. When installed the top of a flooring would look like what a cut nail would look like.
Is you plan to do the flooring the way it looks in your drawing, i.e. kind of like a herringbone? If so, you could cut grooves in the ends of the existing floor boards with a slot cutting bit in a router. Install a spline in the grooves. Put a nail through the spline on every other board to lock down the end(s) of the boards as you don't know how far away a nail is. Then cut the infill boards to the proper angle and cut a groove in the angled end and slip onto the spline. Nail through the tongues of the infill boards and work your way across the room. Will require a lot of cutting and grooving.

The best type of glue to use would be a moisture cure poly-urethane type.
You could also use a latex sub-floor adhesive at the joint between old and new with nails or cleats or staples into the herringbone.

Or a biscuit joiner works ok instead of a slot cutter.

What about this solution? I cannot slot/biscuit due to the possibility of hitting a cleat in the existing installation. Also, the existing flooring has 15# felt under it so if I glue it down as suggested it would not "push under the old flooring".

Would a shiplap joint as per the attached be a possible solution? Would glue be necessary as the now flooring would be nailed 2-3" from the joint and would hold down the existing?

Thanks to everyone for the input.

The latex sub-floor adhesive will glue the edges together. You can undercut the edge of the new flooring to make it easier to get a tight fit. Undercut only the bottom part of the edge so you won't sand through. This will allow enough glue to hold the edges together. You will be fastening all the ends of the old flooring to make sure there it is fastened down. The new flooring will be nailed and then glue at the ends. This should be plenty of holding power to last.

A FF biscuit or a #0 biscuit would work. Even if there are cleats on the ends of abutting boards you would have 1 1/2"+ of cleat free wood to cut a slot in. Ship lap would require some precise cutting.

Why don't you try using a strong magnet to find which nails you would hit and skip those areas with the router and slut cutter

Looks like a biscuit cutter is the way to go. I borrowed one today and it worked great (I had never used one before). Will also try to check for nails near the edge with a magnet. Thanks again for everyones input.