I will tell you that I did slightly enlarge the opening on the cover in the area to the left of the primer elevating pin, just a little bit with a sharp pocket knife . The biggest problem and easiest solution is the angle at which you are holding the tool. I hold it tilted away from me maybe 45 degrees. This is more than enough to keep the primers moving. I have timed my priming and can do 50 cases in just a hair over 4 minutes without busting my britches and now rarely have any problems with "mis-presented" primers.
Another problem I solved is the use of an improperly sized (for the specific case) shell holder. Lee's generally work fine ... but there are some calibers which their dimensions are just too generous and I need something custom. For example .25-20 SS required my taking a regular shellholder (RCBS, I think) for .25-20 SS and turning off the stud and chamfering the underside of the hole. Now my cases don't have to be forceably held in position while being primed. I found this too with some of my 6.5 and 7.35 Carcano (reformed 6.5 X 54 M-S Norma Brass). Reworked a reglar shellholder for them and away we go. I've done this over the years with a number of calibers and it has made a big difference.
Finally, I have a 3/8" or so hole in the top of my reloading bench which is no longer being used for whatever its original intended purpose was, but it's PERFECT for holding the pointy-end of the Lee tool so when you tilt it away from you, the tool can't move around on you ... just like it's locked in place.