I have had a lot of the symptoms you're describing, including that they come and go. When I first got sick, they were always different so no one could figure out what was going on.
If I were you, I would definitely test through Igenex. I don't think it's true that they get a lot of positive test results, as your doctor said. I think the reason they get positives where other labs may not is because their tests are more specific, thereby lowering the chances of a false negative.
I look at "false positives" with Lyme as I would a "false positive" pregnancy test (what an analogy, huh!), not very likely. If someone has a positive Lyme test, regardless of the lab, chances are, they have Lyme.
I had a negative ELISA and 3 bands positive on a Quest Western Blot. The doctor I was seeing at the time told me I didn't have Lyme. I tested through Igenex and more bands came up, CDC positive. I started Lyme treatment and herxed immediately so I definitely have Lyme. But, had I not tested through Igenex, I wouldn't know that.
Sorry to ramble on, I just hate when doctors don't try every avenue to help their patients.