Irishmike: Like everyone so far has told you, with your current hardware you just cant do what you want. I would recomend getting a Pegasos II board and using MorphOS. You could do everything for a lot less money then what it will cost you to get the A4000 (Keep in my that an A4000 will be exactly the same if its stock as your A1200 in resolution choices)and a mediator and an accelerator board. Youo can get a complete ODW (Pegasos II with hard drive, video card and a nice case) for about $500 new from Genesi.
MorphOS will run all the newer apps you want to run better in many cases then a real Amiga if its system friendly, and for the old games you want to run that do not work on MorphOS you have the A1200 that can do that for you.