Well, first thing is, did you plant it in a well draining spot?

I always amend my soil with plenty of compost, peat moss and manure,
so I think it's pretty well draining. Should I add some pea gravel to
the mix as well?

I will say that it may be in spot that's a bit shadier than it may
like. It gets afternoon sun, but is in the shade of a large hackberry
tree most of the morning. Could that play a role to its gangliness?

you could whack the plant back to within half of what it is now, shoot
some fertilizer to it, like Osmocote time release or bloom booster and hope
for the best.

If I cut it back by half, I'd be removing the only good looking part
of the plant. It's the crown of the plant that looks so crappy. I was
wondering whether I could take stem cuttings, basically cut the
attractive foliage away from the ugly crown and start over with the
cuttings. Can you do that with Coreopsis? Or should I cut it almost
to the ground early next spring, removing as much of the ugly crown as
possible, and hope for new shoots from the root system?

Thanks so much for the input.

-F