Well, I spent 4.5 hours tonight with a clay bar and I've made some progress but still have a long way to go. I'm down to the area where the paint is the thickest and have been using my fingernails through the clay to try to expedite the process a bit. I'm hoping that if I put any scratches in with my nails I'll be able to buff them out later.
As a reminder, here's what it looked like at the start:
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Here's when I was just about to call it quits:
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And here's when I actually called it quits after I decided to get a little more aggressive with my nails:
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I've used about 2/3 of my clay bar but I'm happy that I've at least made some progress and there's hope that I can get everything off and it will look decent with just the cost of a clay bar and several hours of my time.