There are a few things to know about thermal compounds and thermal pads that might be of help.
■Thermal pads are better at conducting heat than thermal paste/compound - in some cases up to three times better but at ~10x the cost per application. It is the cost of pads that make paste more popular on CPU's and other places that may get replaced more often
■ Thermal paste becomes less effective as the application of it gets thicker - the primary reason you always want to apply the thinnest layer possible on any surface
So here's where the method you are attempting 'breaks down'. 1) you have cloth in your compound, cloth is one of the worst conductors of heat there is (why we use it to keep cold air off us). Almost any material would be a better filler than cloth (except styrofoam, rubber or some plastics). 2) Too thick of application for the product to perform well.
Here is what I would suggest sans putting in new thermal pads. Use aluminum foil to make a pad, layering on top of itself with thermal compound between layers - very thin TIM layers, you're simply removing air between the layers of foil. Or, an option (I don't think is as good) would be to fill the paste with as much diamond powder as possible (50,000 grit minimum, 100,000 is better but harder to find) without drying it out too much and just use paste. Diamond powder can be sourced through most lapidary suppliers and is not too expensive (~$1/carat). I should point out here that while silver is the best heat conducting metal, diamond is the best heat conductor known.
Hope you can get somewhere with that info