If there is no sign of bug damage where they touch the ground just leave them until the vine is completely dead.

Once the vine is dead and dry there's nothing more to be gained by leaving them attached so, at that point, cure them and move them to a cool, dry place for storage.

Ditto.

to take precausion aboutpossible bottom rotting, put some pine straws under them, to keep dry.
Even after the vines die, the pumkins keep getting mature in the sun, the shell will get harder, the seeds will ripe.

Thanks for the advice everyone.

It seems that my Big Max pumpkins start rotting as soon as the vine begins to weaken. The Jack O Lanterns seem to be hardening and not rotting. I will keep an eye on it, thanks again for the advice.