[Zeke]

It's done all the time. If you have 2" of support behind the top of that drawer and there is room, you can run a 3/4 x 3/4 angle iron behind the built up bullnose. What I'm saying is that you can take some of the cabinet away at the top up to the top of the box. If it's a typical Euro box, there's not a whole lot more room to go up.

Your new unit will want a better platform to sit on, so by all means take out the cabinet floor. A multi-tool like the Fein or HF will be one to use in many places there.