Q: If I have Doctors 7 and 8, and another player has Doctors 3 and 4, and the Goal Regeneration comes up, who wins?

A: Sounds like a classic case of two people meeting the winning conditions at the same time.

On the rule sheet itself, at end of the first page in “Notes” is the ruling for ties:

“The game doesn’t end until there is a clear winner. If for some reason two of more players meet the winning conditions simultaneously, the game continues until a single winner emerges.”

So, for your situation, the answer is actually fairly simple: there were two players meeting winning conditions simultaneously, so keep playing until a clear winner emerges. Note that the “clear winner” need not be one of the two originally tied. It could happen that the game state changes, and someone else wins instead of either one of them.