61.41 covers training under part 61. If you're trying to do a type rating the problem is going to be the 142 school. Each FAR 142 has a list of instructors that can teach their programs. They don't have to hold a CFI, just be on that school's list of instructors. So if you show up with items signed off by a non-FAA instructor the training center will say those people are not on our list of approved instructors and did not teach our program. You can't just say I'll do day one of your program but day two is covered by this guy's signoff. Subpart C covers the requirements for 142 instructors.