Jumping on the conversation regarding travel with the expired GC and letter of extension.
I worked for a large law firm doing immigration work. We never had any issues with clients travelling with their valid passport, expired GC, and original copy of the letter of extension. Yes, it takes a little longer coming back to the US going through CBP and Immigration because they need to verify that your ROC is still being processed and you are still in valid status, but that's it.
My husband and I have travelled to South Africa twice in this manner, no issues, just the extra stop we know we'll have at the immigration desk so they can verify status. I also always bring a copy of our marriage certificate, and we don't travel separately, to help make things faster and easier.
I haven't browsed the whole thread - is anyone else getting ready to file for citizenship while their ROC is still pending?