Your programs are set with native screenmodes, ie not the ones Voodoo outputs, but amiga's chipset. You should get a scandoubler and a monitor switch to have both on your lcd monitor and even then you need a scandoubler that syncs to 56hz or more (there's none for A3000 that I know of, there's only Indivision AGA and that's for A1200 only atm) - the minimum frequency of most lcd displays today - in contrast to 50hz that scandoublers do which was enough for crt monitors and some rare to find lcd models. Unless of course it is a LCD TV, so you may connect the rgb port to scart with a proper cable. That is if the tv has a scart input. Or you may keep both monitors connected.
Anyway, that's mostly important for games that bang the hardware directly as you can set your os friendly programs to use Voodoo modes. So, while you have your old monitor connected, setup your programs so they open Voodoo screens. That's not good enough for DPaint obviously as it only accepts native screenmodes.
You can also install a screenmode promoter from aminet (eg Modepro or Newmode) and try to send old programs that won't let you set the mode yourself to Voodoo (eg Lightwave - won't work for DPaint though).
Good luck!