Place helmet on head. Tap out where helmet contacts your head, echo-ey part is *NOT* where you want padding. Sharp sound is where you want paddding. Mark contact points on helmet with something erasable on outside of helmet like a Sharpie.use Sharpie marks as reference points.
That padding looks SUPER THICK, try thinner padding for trial run. Rough up area where you are going to attach padding. Id buy some 1/4 inch foam.
Velcro sounds good,, it usually comes with peel off sticky sides. I would only use spray if you cover areas you don't want to be sticky -- last thing you wanna do after wearing a helmet all day, is tear out your hair removing your helmet.
You can also use quilted pot holders/heat pads if you are feeling lazy.
...or you could make a copy of your head by putting a thin sheet of aluminum foil, on your head, then apply some Free Forn Air on TOP of the foil. Put the helmet on CAREFULLY. Wear the helmet, FreeForm Air, foil for 1 1/2 hrs. You will feel the FreeForm Air heat up. Now you wont need padding as the helmet will fit your head PERFECTLY.