When you cut it, try propping it up a little on one side - say to maybe a 45 degree angle or so - so that the piece you are cutting off does not fall from the roast as you cut it. Depending on your situation, this may take some ingenuity to make it work right (without dumping the roast onto the floor... ;). As for the knife to use, try cutting it with a very sharp, thin but wide-bladed, long, non-serrated knife. You can use the wide blade to assist in transferring the cut of meat from the tilted roast to a plate when you complete your cut. Experiment with either making very long strokes as you cut, applying very little pressure and cutting on the forward stroke only, or by making very short strokes - again with very little pressure - maybe even cutting in both directions. One way may work better than the other as each technique will torque the meat in a different way. This is also situation dependent - depending on how each specific roast is marbled/etc.. The torque/twisting is what makes the meat fall apart, so you will have to keep a close watch on how your cuts are affecting the meat - and change your technique on the fly as you see fit.
If the wideness of the blade is still pulling too much as you make your cut, then try using a knife of the same style just mentioned, but with a narrow blade. Your cuts wont be as clean this way, but it may be necessary. Additionally, the narrow blade will also make it more more difficult to transfer the meat to a plate when you are done.
If the meat is so amazingly tender, it may also be necessary to place something behind the roast, where the blade exits, as you make your cuts. A small cutting board will work for this task. To better explain this, think of how an electric meat slicer at a deli supports the meat in two places. It supports the meat on the bottom, and it supports the meat very close to where the cutting wheel exits the meat. You want to duplicate this somehow.
If you are still having issues transferring the slice of meat from the "tilted" roast, after it is cut, try assisting your knife with a very thin and very wide metal flipper. To do this, gradually tilt the slice of meat up with your knife, and ease the flipper under it until you are supporting the entire slice of meat with the knife and the flipper - then transfer it to a plate.
There is a good chance that you may be able to successfully use this technique while the meat is still warm/hot (i.e. no prior cool down necessary).
This sounds so delicious you have to send me a slice!