Hi Evan, sorry to hear your frustrations with this.
From past experience I know that the 17 inch flex does not get very hot. When I saw your thread, I went and wired up a few sections just to see what we are up against. It has been on for over thirty minutes now in a room that is 78 degrees and it has reached only 95 degrees using an infra red thermometer directly on the surface.
I will let it run and see how well it does, but I am quite sure that you will need to look into a different heat source for the temps you are trying to achieve.
I checked a chart showing the emissivity of different materials, and while it doesn't specifically state Plexiglas, it does give a very high factor for plastic. Going on that, I think your idea to cover the heating element with plastic is a sound one.
Also, what are you using to measure the temperatures and from what distance?
Could you describe the enclosure setup in detail?
Are you using a thermostat, if so where is the probe placement in relation to the heat source?
This will all be important in order to get things worked out.