How do you keep a carved pumpkin "fresh?"?

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You could try salting it, but this might just make it shrivel faster.

Maybe urethane?

Rub vaseline all over the inside and out, of the pumpkin. That’s what I did to all of my pumpkins last Halloween and it definitely makes them last longer. Make sure you put a really good amount on, though. :)

You said that you don’t have space for the pumpkin in your fridge, but I think putting a large bag of salted ice inside the pumpkin would accomplish the same thing, just make sure it’s sealed.

You can display the pumpkins in their original form until Halloween day, and carve them before it gets dark. Then you can just throw them out (or compost them) once they start to rot.

rub Vaseline or petroleum jelly on thi inside and cut edges.

We’ve stopped carving ours entirely. They last forever that way. We either decorate it or use a sharpe to draw our Jack-o-lantern face on it.