Travel outside US on AP while awaiting AOS for EB-1A

[GC_EB-1A AOS Pending]

1) Would it be recommended or advisable to travel outside of the US, with a valid AP (advance parole) and EAD, while awaiting the final Adjustment of Status (AOS) on an EB-1 A petition?

2) Have People experienced any major issues, hassles, orworse, a denial for re-entry at a major Port of Entry or the border (during additional screening) even with thevalid Advance Parole?
Case Deets:

1. Self-petition applicant for EB-1A
2. Prior H1-B visa has only recently expired in September 2019 (without any lapses, gaps, issues or violations).
3. Switched over to EAD in March 2019.
4. currently on EAD (which has been renewed till January 2021)

I get that since the EAD is not a valid 'status' to be on per se, it could be perceived as risky to step outside the US, while an AOS application is pending? A lot of people, I understand, travel without any problems and have been able to exit and reenter?

Both our personal Attorney, various immigration websites, and/or other attorney websites; as well as on USCIS' site, it states that one may be eligible to travel as long as one has a valid advance parole document.
I was wondering about public perception or experiences?