-I do not agree with your lawyer. You just need to tell the Immigration officer you just need to extend TN for a few months and you will work with h1 status beginning Oct. 1 if the immigration officer ask the question.
Could you please let me know why the option 1 is not good?
-If your TN is approved after Oct. 1, your final status will be TN, no more H1. Then, you need to file an application of changing status from TN to H1 again if you want to be H1 status.