Can I extend my stay in Thailand and obtain a work permit without my final transcripts from a Thai university?

My Ed visa expires the 2nd of march. My university has informed me it could be up to 3 months till I get my final official transcripts.

Would it be possible to leave and come back on the 30 day exemption(American passport) then do a 30 day extension and if needed do a 60 day family extension.

I already have job offers but the contracts would start in April or May. Is it possible to get a work permit/visa without official transcripts if from a Thai university? Or am I at the mercy for my university to get my transcripts before the start date and risk it?