I'm taking the mat off because there is a lot of it and when sand-/glassblasting, it could be a problem (and drive the price up).
My modus operandi is that I heat the mat with a heat gun and then scrape the mat off with a metal scraper. Slow and tedious work, but my time is free compared to the blasters time. Another way would be freezing the mat, but unfortunately the weather is a bit warm for that and I'm not going to buy dry ice, if heat gun does the trick.
After all is said and done I'm thinking that sound proofing mat should be installed and for example Dynamat could be a solution. This will need some thinking and researching as I would not like to add a lot of weight to the car... also not introduce another potential rust problem.
See Taking Zeta apart - Part IV