I just ordered a "Deep Scratch" resurfacing kit from Eastwood. Looks like it will do the trick of removing all of the tiny pits, scratches, and other blemishes from the windshield. The kit has grinder disks and polishing compounds that actually remove tiny amounts of glass to take the surface down to a new, fresh one.

I'll let everyone know how it goes and the results.

Cost of a new windshield: $300.
Cost of kit: $53 delivered.