After running several tests with different filaments, speeds, temperatures my issue has essentially come down to a "Bad Slice" with Slic3r as I ran the same model through Kiss Slicer and everything worked beautifully.
It turns out that the issue was exactly what enggmaug pointed out where it was trying to extrude 100mm instead of 10mm and the hot-end was getting gummed up.
I've found that Slic3r handles manifold models quite well, however, when feeding it non-manifold models things tend to become quite dicey. This is understandable as slicing non-manifold models requires the Slicer to make several assumptions about what you actually want and the math just doesn't always work out for the best.
I found that Cura actually has the best support for non-manifold models in that it allows you to configure how sub-models and cavities are dealt with within the Expert Config section of the tool.
In my case I had created my own supports and baked them into my model file as I wanted to see what the difference would be between a custom support structure and the standard ones that are created automatically. My supports were made up of many interpenetrating posts and struts which ended up working out well from a removal standpoint, but obviously caused the software a bit of grief. In Cura I used Combine Everything Type-B which sounds like it only raycasts the models exterior while slicing, which is exactly what I needed.
The model ended up printing well in Cura, however, Cura doesn't appear to offer the option to set custom Extrusion Width which is a clear issue as I've calibrated my Extrusion Width and Flow as per Polygon Hell's tutorial (
http://forum.seemecnc.com/viewtopic.php?f=54&t=1163 ). I've since printed the same model in Kiss Slicer with stellar results.
I suppose the moral of the story is that every slicer is going to excel in different capacities and it pays to know all the slicers out there, it's really easy to run things through a few different slicers when you're having trouble and choose the one that works best.
The ultimate solution though, as enggmaug pointed out, is to understand enough of what's going on under the hood to at least figure out what the problem is and either ignore it and use a different slicer ( which is what I've done ), or fix it yourself and continue on.
Thanks for all the help with this issue, you guys make up a great community.
-jon