I am no expert; I've only overhauled 4 Raleigh 26tpi BBs, but I encountered a similar situation on one of the Raleigh Sports. The cups were fine, new ball bearings, and a nice unmarked spindle. My solution was to tighten the cups a little more than needed - the spindle felt notchy when turned by hand. Once the cranks were installed, it turned smoothly. Although a little difficult, you can fine tune the cup once the crank is installed.

Also, I can attest to the efficiency of the fixed cup remover tool that Bikesmith Design sells. Like the others, however, I don't think you need to remove it.