Youre complicating things for yourself. You need to align to School's admission schedules rather than you OPT. Find the college requirements first. Admission process itself takes months and deadlines usually are more than a month out.
Your priority should be to get a I20 and transfer your SEVIS for Fall 2019 or Spring 2020. Once you have a signed i20, you still get 90 days to actually start the program. March 2019 may be a bit of a stretch because your 60 initial+90 days start date will expire. 90 day clock starts when you get your new i20 signed.
For TPS EAD concerns, you can just apply for TPS reinstatement first without EAD. Wait for approval then apply EAD later.