Thanks for all your help everyone! We've decided to make the stay at Kidani!
We actually emailed a copy/paste of our questions from here directly to the company, and received a response from the wonderful lady who is taking care of our booking. For posterity's sake, I would like to copy/paste her response here for others who may harbor the same concerns as us.
The letter reads as such (sorry for any formatting issues):
First, be assured that there are countless safeguards in place to ensure that doesn't happen. First, the reservation is made in your name and you will link it to your MyDisneyExperience account, so you will always see that it is still there. Second, we verify it in several systems on a regular basis to ensure it is still intact. The Member is contractually obligated to provide the Villa and they want their money. It's a mutually beneficial relationship and we've NEVER had a guest show up to Disney without a room. In the
extraordinary event where something does happen, you would not be out your money. We would work to find an alternative option and your money would be refunded. But as I say, even that happens so rarely, a handful of times in the entire history of the company. The room is NOT in the owner's name - the room is in YOUR name so MyDisneyExperience works the same as usual. You will receive a confirmation # that you can link to MyDisneyExperience and everything will show up there as it would for a regular resort reservations and all the benefits of being a resort guest are included in that, such as making FP+ reservations 60 days in advance. You can purchase your tickets from whomever you choose and you can link them to your MyDisneyExperience account so they will be linked to your MagicBand. I would be happy to help you with those as well. You will set up Magical Express through me. I will send you a link once you have your flights booked. Hope that helps! Please don't hesitate with any additional questions. Your request has gone out to a Member so I will have your confirmation details shortly. Thanks again!