EAD use, require urgent advice

GCforTRAVEL

Registered Users (C)
Hi,
I need some advice urgently:

I have an approved I-140 based on NIW. I-485 pending due to retrogression.

In 2006 and 2007, I have re-entered USA on 2 separate occasions using AP and continued working on valid H1-B petition according to Cronin Memo.

Right now, I'm in PAROLEE status BUT working on H1-B petition, NOT EAD.

I'm now about to change jobs now. My new empolyer says they do not recognize Cronin Memo since it is not law but a memo of guidance. Accordingly, since I entered on AP and am in PAROLEE status, I should use my EAD.
Work is in same area as my I-140/NIW work in a govt. research facility.

Is it okay to start working on EAD?

I'm aware of all other discussions about how staying on H1-B is a safety new i case I-485 is denied, etc., but my new employers maintains that this is hardly a safety net since Cronin memo is gray area and very controversial.
 
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