Tying a new framed wall to an existing house. Straps cannot be used and top plate cannot overlap at the joint

Do you have a doubled stud on the in side wall? I would lag bolt together although you should figure a way to overlap the plates.

You can nail the new stud to existing stud with 16d nails. If you toe nails one up and next down this will make a lock. Would do this about every 2 feet with toed nails about 6'' apart. Example: 6'' from top toe up, move down 6'' toe down, move down 24'' toe up.etc

Chuck