I don't have the same problem with rc paper off the roll (single weight) as you describe (until I get close to the core), but I do have a serious problem with my double-weight fb off the roll. Like Matt, I cut to size, place in black plastic photo bags, and leave under weights for weeks or even months. I have learned to work with the curl rather than try to fix it. I manage to crease the paper if I reverse curl or pull it over the edge of the counter.
The key for me is to use earth magnets on the outside blades of my Saunders easels and a steel bar on the bottom blade. I find this holds even the worst of curled paper flat to the easel bed. The steel bar is easy to remove when it comes time to remove the sheet, and I can easily lift the blades with the magnets left in place.
As K-G said, once the print is in the developer, the curl disappears. I use 2 liters in an 11x14 tray, place the print in the developer face down, and gently hold it down as I rock the tray to agitate the developer over/under the print. I find that after 20 seconds for fb paper, I can turn it over and watch the image appear for factoral controlled development.
Having described my methods, I would still recommend buying sheets over rolls. With the prices that I have encountered in the stores, sheets are not only easier and less time consuming to work with, but they are actually cheaper! I have multiple rolls because I took advantage of the opportunity to buy fresh rolls (100'x56") at $99 each . Subsequently, I do lots of experimenting.