I have an update. The Danby 6,000 BTU A/C appears to work fine with my set up. I ordered one from a crook on EBay, but he never shipped it or responded to emails until I opened a case to get a refund. I ordered a second one from Home Depot after I got a refund from EBay. It was cheaper but took two weeks to get. They took their time mailing it from Arizona (4 days until they put it in the mail), then there was a holiday so UPS put it in a warehouse for another 4 days.
Here are my test results:
The first test was to let the van idle with the A/C on. The voltage was stable for almost a half an hour until it gradually decreased. The internal low voltage alarm in the inverter went off. It ran for a few more minutes until it shut down.
The second test was today. I had it on while I was driving, but I only did a few short runs so the A/C wasn't on for that long. The voltage on the dashboard was pretty stable except for a few intermittent fluctuations, but it pretty much remained in the correct range. The inverter maintained the correct voltage as well as the alternator, so the A/C performed as it should. I haven't tested it for long driving but from what I could tell, the charging system is able to keep up with it for basic runs around town. I would like to test it for a 30 to 45 minute run at some point.
The A/C has a built in time delay, so the fan only runs without the compressor for a few minutes when it starts. The compressor kicks in after this time delay. This gives the charging system a few minutes to charge the battery when I first start driving.