OPT work

If I used up all my OPT/STEM years by doing postdoc, what happens next? Do I have to find an academic position afterwards? I mean since I would not have time apply for H1B, I can't transfer to industry, right?

to Lily:

What about O-1? With PP, the process is super quick. Sometimes employer sponsors both O1 and H1B so you can try H1B first. If you failed, then file O-1 immediately. (But still OPT expiration date is crucial)
Or, you can transfer to non-profit H1B and stay with your current employer until you get the green card.
Another option is you can transfer to J visa if your university does not sponsor H1B. J visa's advantage is your wife can work with J2 EAD.
The most ideal scenario would be: You can submit EB1A I-140 and when your PD becomes current, you can change employer with I-485 EAD.

to Lily:

Lois' suggestion is generally correct, but do mind that if you have some sort of visa, the moment you use 485 EAD that visa is going to gone. And if you get really unlucky and 485 is denied, then well.....you don't have visa to stay anymore.....

I'd try to get some kind of visa if I were you