Hey @Jason Lohse! Lots of good info from you in here, and I would definitely stay away from renting down here in Denver if you can. However, I believe there is a way to get away with not selling either property. But let's work through this together.
1. For The GA home you wouldn't have to 1031, as you occupied it as your primary two out of the last 5 years. So you are exempt from $500,000 in capital gains tax.
2. STRing the Fairplay home is an option, depending on if it is in incorporated Fairplay or unincorporated Park County. Either way, you should be good, unless the last few Fairplay licenses have been snagged. I am happy to check this for you!
3. Your 40-50k in DP is enough to get you into a reasonable place here in Denver, as long as you are qualified buyer. Using a low downpayment loan, you'll be able to get into a 500k home reasonably easily.
4. I have plenty of banks that will do HELOCs on investment properties, but also, is their equity in your Fairplay home? You could pull a HELOC up to 100% (I suggest keeping it at 90%) since it's your primary. I would definitely recommend this if possible.
Personally, I think you are overthinking it. You are in a great position and should have no problem getting a place here in Denver, and there are ways around the leasing of your Fairplay property, if necessary. I am happy to dive into the details with you, but I wouldn't think about selling either property at this time, and I wouldn't put too much stock into you Fairplay home value being down at his point.