This is really not a DIY project.
From your description it does sound like a poor installation.
A properly installed drain should be sumped lower than the surrounding roof level.
Ideally the drain itself should be a 3 piece drain. A drain bowl, a clamp ring and a strainer. Also a lead drain pan should be installed.
DO NOT use Ice and water for the cap sheet. It is not designed to be exposed to the weather even it is covered with gravel. It will quickly deteriorate and cause some real problems.
Click the link for an example of a proper roof drain installation.
http://www.fieldscorp.com/commercial...tails/fd01.pdf
You'll see it is alot more involved than just cutting a hole and burning new around the hole.
I would seriously consider calling one of the larger commercial roofing outfits in town for quotes. PLEASE do not have a residential roofing company look at it.
I'm with a large commercial outfit in the Service Division. In our area installing a drain like this would take 2 men 4 hours at the MOST.
For about the same price you paid for the first one. But it would be installed by guy's who do this every day.
Low slope roofing and steep slope roofing are two different animals.
I do not dabble in the shingle division because I know flat roofing. I pass on shingle work to our Steep slope division. They do the same when they come across flat roofing.
This is just my $.02 worth. I've seen enough penetrations badly to know what kind of nightmare it can turn into.