The problem is I really suck when using poly. I either put it on too
thin and get areas where I miss or I put on too much and I get areas
of varying thickness. I've tried to let it set up a few days and then
sand, but the sandpaper gets all gummy. Maybe it needs a few weeks to
cure, I don't know.

I just re-finished a chest with poly using a method from Wood Magazine.

Sand wood to 220 grit.
Apply a light coat of poly. Let dry Sand lightly with 220

Apply a second coat. Let it dry for 2 full weeks.

Wet sand with 320 grit

Polish with pumice

Polish with rottenstone (it will look kind of dull)

Wax with paste wax

This is the best finished piece I've ever made. It has a satin sheen, is
very smooth.