A couple simple ideas to mitigate rushing

This isn't supposed to be a long, drawn-out thing, and maybe it's been discussed before –

1. Nobody can get in or out of the basement for the first minute

Victims can still grab tools, bone scraps, etc., but are unable to lockpick the doors. At the same time, Family cannot gather blood for Grandpa in that time either. After the minute is up, the doors can be lock-picked and blood can be gathered.

2. Family starts in better spawn locations

This just goes without saying. They need to spawn closer to the objective.

I mean, that's really it. Most rushing is due to Family not being prepared as the victims bust out of the basement. Keeping them in there for at least 60 seconds will at least give Family time to prepare before even the fastest victims bust out.

That's really it. The map design doesn't really allow things to be shuffled around so the best option is to keep the first minute of the game restricted to the basement.