At what point does it become too late to find a new doctor?

The sooner the better weeks: Some doctors will not accept a new patient after a certain time which they determine on their own. I would suggest you look for a new doctor as soon as possible.

<=28 weeks: Usually you should have selected an obstetrician and received prenatal care since early to mid first trimester. With individual exception, you usually will not be accepted by a new practice entering your third trimester (about 28 weeks). This is because the accepting doctor has additional risk in caring for you and it is often too late to correct problems he/she may have addressed earlier.