I have removed the internal coating on a few old Canon and Leica lenses. The process is simple enough, but it can be a little tedious. First, I dampen a cotton swab with a bit of lens cleaning solution, then I add a bit of toothpaste. Then I begin to polish away the coating using a circular motion. Depending on the type of coating, it can take 10 minutes to an hour to polish it all off. The toothpaste is abrasive enough to remove the haze, but does not harm the glass. I have saved some pretty rotten-looking lenses using this method.
I've used this method on several lenses with no observable change in lens quality(flare maybe?). Latest one is a 100mm V-Elmar.
The element is NOT too thin for this treatment, if you're using toothpaste. I use a tiny tube of Colgates I've had for at least 20 yrs. I just use my dainty index finger for the polishing bit and common lens cleaner for the last cleaning.