Hi, no reason why you shouldn't be able to drill the rivets out.....sometimes they will need a decent smack to help them along their way. I generally drill the rounded head off after running a pilot hole deep into the rivet and following up with successively larger drills until the head falls off,then run a drill marginally smaller than the rivet dia. part way into the rivet body, but not all the way through.... ( make the hole at least as deep as the rivet depth) to relieve internal tension within the rivet,then use a decent size punch and hammer and give it a few solid whacks ,that should knock them out.
If you're going to cut the frame rails,best plan is to keep the cut ahead of the crossmember or maybe even join it through where the front crossmember is riveted. It's not a great idea to weld channel section frames, especially in the areas of greatest stress....like from the crossmember back. Vertical joins and welds are supposed to be avoided when joining frame rails, and cuts are meant to be on an angle and then covered with a fishplate....which looks totally trashy ,so most guys don't do it. If you made the cut and join in the area that's covered by the little radiator mounting bracket , the bracket itself will help to bridge the weld repair area somewhat , and if you do it neatly enough.....no-one should ever notice it, regards, Colin.