I wasn't that far along, but I switched shortly after the gender scan each time. The first time was due to an insurance change, I was something like 24 weeks. And I LOVED the new office sooo much better, as it turned out. I wasn't happy exactly with the office already, it was a 2 doctor practice and while I liked my doctor, I hated her partner. And the lady at the desk who scheduled appointments was really shitty that I would only take Friday appointments (That was my weekly day off). I was nervous about switching, because it was changing hospitals and everything, but it definitely was great.
The second time, I started at one office because not only had I moved, but I had no insurance at the time and they did a cash discount. I loved the staff completely and once I got insurance, I didn't plan on changing until I found out that the hospital they delivered at did not allow VBACs at all, not in any case. They would only do a cesarean at 39 weeks (or earlier!!). So even though it was further away now, I transferred back to my other doctor (my second office). In the end, I never went into labor (and they won't induce a VBAC) so it was a second cesarean at 41+1. But at least they were going to let me try!
That third doctors office I would've stayed with had it not been for the hospital policy (the doctor herself told me that she would personally recommend the VBAC but she wasn't allowed to) but my baby got to 'bake' for two extra weeks because of my change.
Ask for a copy of your medical records in advance, or if possible, have your new office fax over a request for records. You'll have to sign to approve the request, but in my limited experience, they transfer records directly to the new office faster than they get a copy to you.
Good luck and I hope you love your new office!
