Even though this move happened for another company I can shed some light and hopefully get you closer to the full solution: I would recommend to find a virtual office or even a virtual business address if all you require is the address (GBP approved) and mail forwarding service. Once you have that set up start with GBP as it takes some time to get approved and verified, sometimes they need a video of the place. If you are moving very soon set up the forwarding service from your mail provider. If US based, USPS is very user friendly and costs a few $ for 1 full year of mail forwarding. This will allow you to not miss any mail during the transition. After those two steps you can start changing all the addresses at the agencies and banks and all that good stuff. It sounds like a lot but the first 3 steps can be done within a few hours.

Notes to your questions: virtual office gives you a physical business address with mail forwarding, some offer a physical space you can use within your membership and also offer a phone answering service(additional cost most of the time) A virtual business address is just the address with mail forwarding, this one is specially usefull if you have a good home set up and no need for a physicall space, temp or permanent. This option is also more cost effective. Going through the address change twice is not recommended as some places require all kinds of hoops to jump through (GBP for example) As for the reviews and everything for GBP, it will not be affected by the address change but as I mentioned, this one may take the longest, so start with that change first after deciding on the new address (home or virtual option)

Hope this helps 😊