Adjustment of Status - I-485

Hi all. I have a few questions/I need advice as I think I have a sort of complicated experience. I am married to a USC and finally got our rescheduled AOS interview for Aug 17.

I recently got a job offer from the United Nations. When I applied they specifically asked about my immigration status because they said they can sponsor a G4 visa for me if needed. I told them I'm in the process of adjusting my status to permanent resident soon. So I got the job and started with my onboarding 2 weeks ago. HR asked for my foreign passport and greencard 2 weeks ago. I sent them my EAD instead and they went on with the hiring. Everything went smoothly and today was supposed to be my first day at work but before I can even start, the department head called me and said I can't officially start because I am not a permanent resident nor a G4 visa holder. I explained to them that the EAD should be enough but they said that this is a special case, unlike other US companies, the UN has an agreement with the US govt to only employ people of 2 immigration status: US citizens/permanent residents or foreign nationals with G4 visas. I am literally in the middle. When I told them about my upcoming AOS interview in 2 wks and the best case scenario of USCIS approving my I-485 on the spot, they said they'd wait for me. They just want me to get that in writing, in case I got the AOS approval, so I can immediately start working for them.

My questions are:
On August 17, when they give me an on the spot approval, how can I have it in writing? Will they give me a paper that says something like that? Those who received their greencard, is the effectivity date of your AOS the day they approve it? In my case, hopefully Aug 17.

I'm a little bit stressed about all these. Applying for this job was stressful enough and then the whole AOS process that my spouse and me have been waiting for for about a year now. Anyone with a similar experience?

Thanks a lot in advance.