How would I produce (stable) foamy bechamel sauce?
I ended up getting the recipe from the chef himself! It turns out that gelatin makes little sense at the temperatures involved unless you up the quantity in which case the texture gets altered for the worse (I experimented only twice so I can't really be sure that it wouldn't work at all). 

The recipe itself calls for a bechamel with a very light roux simmered for a very long time (~3 hours) and stirred occasionally so that the milk doesn't burn. At the end of the process it becomes thick enough to foam in exactly the right texture. Strangely the guy doesn't use any seasoning aside from salt and pepper but I'd think this is so that the particular dish is in balance.