Update
Just wanted to take a moment to thank everyone for the tips and info and provide an update.
After finally obtaining ppr, the trip went smoothly. The company had the permit request in for 10 weeks, before it was issued 12 hours prior to departure. No reason for the delay was given, or I suppose it could be that is normal for this location. The AFIS was manned and operating for our arrival, but there was no response for departure. Wasn't able to contact San Francisco radio on the ground, but was able to reach them via cell phone in order to obtain a clearance. I had a US AT&T phone that was the only one of the crew phones getting any service on the island. If your Sat. phone equipped, I would recommend confirming it will work on the ground before operating there, or renting a hand held. I wouldn't count on cell service. Fuel was provided as requested, but it did require careful coordination with the ground handler after arrival. I'm not certain it would have gone smoothly if we were attempting a quick turn, as the truck drives approximately 30 minute to get to the airport from the fuel terminal in town (London) on the other side of the island. The runway should be repainted by the time this is written, and lighting improvements are underway. The runway itself is in good condition. The terminal building appears to have been recently rehabilitated while small and basic, is in good condition. The flight attendant had packed a large cooler with catering and blocks of ice for the departure, which turned out to be a terrific idea as I don't think we would have been able to source any on the island. After a 5 night stay, it was still cold and usable.
If staying on the island, there are not many options, and I would recommend bringing at least a few days of bottled water, in order to give yourself time to source some locally. There aren't many options for accommodations. The Captain Cook hotel is about 15 minutes from the airport, but is relatively isolated. There are about a dozen guest bungalows, but no more than 8 of them are habitable. They are rundown, but clean. Another guest told me that there was no running water in his bungalow, but all the crew rooms had running water, and adequate air conditioning.
With a little planning, CXI doesn't pose any insurmountable operational issues.