Think this depends on your risk tolerance. I'm facing the same issues for my parents.
If you can go, I'd go with a lot of evidence, with ties to the US, including tax returns, bank accounts, and your biometrics and notice letters to prove intent of returning. You can argue that you came in under the year mark, to stay legally compliant, even though you have a reentry permit pending.
The risk you run is if your Re-Entry permit is denied, being away a year is abandoning your green card.
To give you an idea, my parents entered the US last month, 11 months after their prior visit and got their green cards revoked and issued an NTA. My dad had a pending re-entry permit (ironically it was approved a week ago) and my mom just had hers expired 2 days before entry. We messed up by having my mom travel after expiration, but they were indeed out for a while. My dad provided a copy of his notice not the original (that's with me) and had a copy of my US passport. It's the only evidence we gave, and was very weak and my parents with their bad English were unprepared. We got super lucky as CBP made a clerical error and gave back their green cards the next day and cancelled the NTA but it gave us the scare we needed to be prepared.
I'm assuming your REP will get approved in June, if everything went well, you can pass your 1 year mark and be fine, if it is denied for whatever reason (unlikely unless you weren't physically present when applying but who knows), you're going to need to apply for that SB-1 visa and chances of approval are none.