Your post is hella confusing.

From what I understood here's my suggestion.

F1 and F2 are statuses , TPS is not.
You can have (TPS and F1) or (TPS and F2) or (illegal and TPS), so there is that.

While you are on F1 you can still work on EAD via your TPS. No need to mention to your DSO (not his domain of interest).
While on F1 you can also qualify for reduced course load so you can take only one class per sem if that helps.

Regarding the last paragraph --
Again , F1 is a status and TPS is not. If you give up your F1 you will be and illegal immigrant with a TPS status (which just means they cannot deport you for being illegal.)

I have heard mixed reactions from DSO's regarding changing status from TPS to F1.
It is absolutely possible to reinstate an out of status F1 with TPS back to F1 but that's a whole another Mahabharata right there.