My contractor's work on draws so they always have some skin in thegame.

Be careful when you say 'skin in the game' regarding a syndication.

Check out this link: Burn Exposure Chart (antiscald.com)As you can see, having skin under 140 degree water can (and will) cause 3rd degree burns in around 5 seconds. 

Do you mind sharing specific/rough pricing for such calls: 1) small things like a drywall patch, 2) to bigger things like a furnace/water heater repair, 3) time-sensitive things like a burst pipe or water-heater out, 4) anything else. 

What would be the incentive for anyone to fund you, if you don't have any skin in the game, if I understand it correctly, and an investor will not even get the first lien.

Make sure you each have some skin in the game (your plan sounds great with him spending $250k on materials and you financing house) so that way it is in everyones best interest to show up and get to the finish line.

Nonetheless a house hack will be a great education for your first rental, it will allow you to get some skin in the game at a lower initial cost, and can be a property you move on from in a year or two and repeat with your next home.

Lots of ways to skin the proverbial cat in this industry!

Since these people have no skin in the game, what might be a good strategy for approaching them to see if they can relax some of the restrictions/prices so I can rehab these properties and get them back on the tax roll?

On FB I have never found any good groups, mostly people just complaining about guests who get under their skin, nothing productive.