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VolvoGirl, thank you so much, this answers my original question. You helped me out a lot. I have one follow up now, though...

(I successfully inputted the $300 extension payment I made in the Fed Section and it flowed to MA section, all based on your instructions, and now my MA state tax section says I owe nothing, so my previous crisis is averted!!!)....... but now I printed out a draft copy of the return to review before the last step of actually filing it , and the cover pages for both of them say the due date is May 17, 2021, but I already obviously got an extension for both of them obviously. 

Do I need to inform TurboTax I got an extension and the due date is really October  - where/how do I do that? In case the answer is 'I should leave it as is and ignore the discrepancy on the cover pages', filing it even though it says Due May 17, is IRS/MA State going to run a check and find it suspicious?

I also have screenshots of what I'm talking about...

Thanks SO MUCH!!!!

VolvoGirl you are a treasure to all these people stressed out about their taxes, replying so fast and answering tough questions.