H1B transfer questions

[niwsas]

2003 - 2009 - F-1 student status - University A

2009 - Cap-subject H-1B filed (April) and approved (September) for work with Company A

2009 - 2012 - H-1B with Company A (H-1B visa stamp in passport)

2012 - 2018 - F-1 student status - University B

2018 - Jul 2019 - OPT with non-profit University C

July 2019 - Present - H-1B with non-profit University C (adjustment of status; no stamping; H-1B visa provided till 2022)

2020 - Self-sponsored EB-2-NIW green card petition submitted - I-140 approval pending. 

Cumulative time spend on H-1B till today = 3 yrs and 11 months.

I understand that I will be able to continue working for a cap-exempt employer/institution using the remaining time (~ 2 yrs) on my cap-exempt H-1B. My questions pertain to switching over to a for-profit cap-subject employer. Any input on the below is much appreciated. 

1. Can I submit a cap-exempt H-1B petition to work for a new for-profit/cap-subject Company B, to avail the un-used 6 yr maximum time period?

2. The last time I was in cap-subject H-1B was in 2012. As it has been more than 6 years since I previously held the cap-subject H-1B visa, I wanted some clarification. I read a recent article suggesting that the DHS has clarified that recapture of unused H-1B time can be made at anytime and there is no time limitation. In the article below, please read paragraphs under title “RECAPTURE OF H-1B TIME”. Does this mean that I can submit a cap-exempt H-1B petition to work for cap-subject company B? Can you please confirm this?

"Retention of EB-1, EB-2, and EB-3 Immigrant Workers and Program Improvements Affecting High-Skilled Nonimmigrant Workers" - Homeland Security rule - 11/18/2016 - Federalregister.gov

3. If I wanted to submit a cap-exempt petition for work with cap-subject Company B, would this be a H-1B transfer or a new H-1B application.?

4. If the current administration suspends H1B visas in the recent future. Will this affect my ability to secure a H-1B to work for Company B?

Thank you for your response!