I was in your exact shoes last year with the same worries. I ended up reading a very helpful guide on how to transfer flight schools and it made the process so much easier. What I liked about their approach is that they explain exactly how your logged hours carry over under Part 61 or Part 141 rules. They also give you a clear, step-by-step checklist on how to request your student records and get a proper logbook evaluation. It really helped me avoid extra costs and saved me a ton of time during my transition.