Can a long-distance investor be considered materially participating in their STR property?  

There are tons of valuable posts, learning materials, and great individuals here on Biggerposckets- so this is already a good start.

If there's a material issue with the property, it's not going away if you cancel your agreement, they'll have to deal with it for the next buyer, too. 

Estimating material costs is easier but the labor is tough.

Yes, there is an argument made that they have to disclose anything material, but that is subjective.With that said, a red flag that came up recently for me when investing out of state was when I was in escrow on a property that was purchased just a few months prior.

Any reputable contractor has material accounts everywhere and doesn't expect to be paid for labor S/he hasn't yet performed. 

Supposedly its all the books and materials but without the mentorship.

External is usually where they want to approve the color of the house, types of materials, roofing, landscaping, driveway condition, etc.

Do you have credit cards with places like Lowes and Home Depot that you can use to buy materials now and not need to pay off for maybe 90 days?

You can avoid alot of issues by sending out an email for example if you have a materials delivered and the guy is temporarily blocking the driveway or taking up a space.