I got a turkey fryer on craigslist, and had the same problem. I couldn't even maintain a boil without the lid at least 1/2 way on.
The ring on my fryer wouldn't support the keg either, so I got a grill grate that lays over top of the ring, and my keg sits on that, so same issue with burner height.
I did raise the burner height. Made a bracket out of angle iron, and mounted it above the original mount, but that didn't fix my problem either.
I purchased a 30psi regulator, and all I can say is WOW! This thing kicks! I had such a vigorous boil, I couldn't even get my march pump to prime. I didn't upgrade the hose or burner.
Here's the cheapest place I found it...
Good CS and fast shipping.
Try using the 30psi reg, without adjusting burner height, I think I have to lower my burner now, since the fame is so much larger.