TL;DR If you make an excel template, limit your named ranges to as small as possible
Alrighty, so after a few more days of troubleshooting, @phildunlap took a look at my excel template. He determined that the named range I designated in Excel was too long (only by a million cells!) for EACH named range, of which there are about 50. So, the theory was that the POI Apache plugin that allows Mango to interact with Excel was loading these empty cells into memory somehow, and was sporadically causing a memory leak or memory usage at least until the point where it would cripple the amount of available memory to the JVM to VERY VERY low, and render the garbage collection useless. Thats a mouthful.
And so, the problem only reared its ugly head once in awhile, it was hard to track down, but I've been operating for about a week now with no "crippling" memory issue, and I've launched thousands of reports without issue. For anyone who wants to know, the final template filled in is 82kb, has charts and 5 sheets of data, the time range spans 14 months and there are multiple different time ranges used and approximately 10-15 data points queried.