You can't appeal an medical opinion. The best you can do is provide the VA with a different one. You certainly can't appeal medical evidence, again, you'll need to provide them with new evidence. If they have opinions and evidence they trust, they won't go looking for more.
Some go so far as to pay out of pocket for tests and second opinions. Its hard to recommend this. As a general rule if they need a new test they'll order one, so these fishing expeditions don't pan out as people want sometimes. Some docs are known to write up some very suspect opinions with no medical justification. Without proper backing for their opinion, the VA simply ignores them. Asking your PCM or TRICARE for a second opinion can be successful sometimes.
It sounds like you don't have a CPAP as they didn't think you had sleep apnea. Likely the best route is to continue to complain about the symptoms until a treatment is found that works. It wouldn't be too surprising for them to come back to sleep apnea and a new sleep study if nothing else pans out. While this might not be great for your timeline, I think its the best way to approach the problem.
I would note that disconnecting wires isn't at all unusual during a sleep study. The sleep tech reattaches them and things move along. My understanding is they help detect when you hit different levels of sleep and are not for detecting an apnea event, so I doubt this is really an issue in your diagnosis. There are many reasons for sleep problems and sometimes people are confused that snoring is the same thing as apnea.