You will have a very difficult time and possibly create a dangerous situation by cutting the acrylic with a dremel. You certainly can use a Hammond box in the manner you describe, and you can still stencil the hole patterns onto the steel with a pencil through the acrylic, I just wouldn't cut the plate up. Since there is no power transformer to worry about, you shouldn't have any compromise in sonics, but you will probably need more wire than the kit came with.
In order to fabricate all the holes you will need:
1/8" drill bit
1/4" drill bit
3/8" drill bit
5/8" drill bit (probably a forstner is a good choice here)
Using the 1/8" bit as a pilot for the other holes is probably a good idea, and to make the holes for the RCA jacks line up well, consider a marking tool or at least a piece of graph paper temporarily affixed to the metal case to act as a drilling guide.