USCIIS clearly mentions that you can not apply for multiple OPT for same degree. However, you can use any amount of CPT , under which you are eligible for H1b ( have friends who got H1b under CPT). College who provide immediate CPT may not be legal (theoretically , student should be enrolled in that university at least for 6 months to get CPT), but its eventually their responsibility. You are still eligible to apply for h1b based on the CPT from those college ( have a colleague who got h1 from similar college).
Regarding TPS, it seems like your employer should be able to apply for your GC as long as you qualify ( like you have bachelor or master equivalent), despite the fact that TPS it self does not guarantee any status ( based on USCIIS).
Some one mentioned that you can come back to F1 after TPS expired. That is true only if you have not maintained the F1 or H1 continuously. Otherwise, you have to leave the country to get back to status, where probability is pretty low .

If I were in your situation, I would not leave my status at any cost. It's just not worth it . I have heard different opinion from different immigration lawyer regarding TPS. So , if it's possible, maintain your status even though you apply for TPS.

those were my golden 2 cents for you.