Relocating late in pregnancy

Has anyone had to move (either out of the area from their original OB or out of state) after 30 weeks of pregnancy? I'm moving out of state at 34 weeks and I'm concerned about the process and possibly being turned away.

Just a little history:

I recently tried switching OB due to a change in insurance (no longer in network) and signed paperwork to release my health records and switch care. The potential provider has not tried to update me in any way. Baby and I have been deemed healthy up until now. Currently I'm 29 weeks.