I've had this problem too. I think that the false front idea is the best way to go. But I have achieved good results doing a larger card front with 2 techniques. First, cut the blank edges off your folders. They still work fine and the resulting crease marks from folding your cardstock around the folder are closer to your card fold.
Second, when you reposition the folder for the second pass through the machine, place the edge of the folder that is next to the previous embossed area on the very edge of your cutting plates so none of the previously embossed paper is between the plates. I even leave a small silver of the folder off the edge of the plates to be sure. Leave this edge as the last part of the sandwich to go through the machine. Then none of the previously embossed portion gets squished. With folders that do not have motifs that go right to the edge like polka dots or some stripes, I've managed to get a completely seamless piece. With dots, you can even line up the previously embossed dots with the first row of the folder. I think I see a video in my future. I got a very lovely comment on my videos from someone who said I was a natural teacher and should do more. Made my day!