H1B Cap Exempt to Cap Subject

[salzburry]

Hello,

      I am currently on a cap exempt H1b visa for past 3 years working for a nonprofit organization. My current employer has filed for an extension for another 3 years which would be approved in a month or so. He is also willing to sponsor my GC in the EB-2 category. Although the pay is not that good. I wanted to shift to a different company for better pay although their H1-B might come under the cap subject category. I wanted some opinion as to how should I proceed. 

a. Should I only target H1-B cap exempt jobs 

b. Should I let my current employer file for my GC and try to change jobs after I get my I-140 approved.

c. Are there any other ways to do it like changing my visa status.(e.g changing to F1 or others)