If the issue is the reach of the brake caliper arms, there are a number of longer (once considered "standard") road bike brakes available. Shimano jumped into the arena several years ago with their BR-R600 calipers which are basically Ultegra brakes with longer arms. Tektro has a great set which look very similar and in fact have a more shiny polished finish, and just a couple minor cost saving concessions which do not efect the overall performance at all. They are less than half the price, and on the ones I had bought, I was able to completely and instantly remove the painted-on Tektro logo with just a dab of nail polish remover to leave simply a beautiful finish with no brand name advertising.

As for nutted versus recessed mounting bolts, I have reversed the rear and front calipers as already recommended. The longer front bolt passing through the bridge really does not need to be cut shorter on many bikes.
This is a modern "front" dual pivot brake caliper intended for a recessed bolt through the fork crown. Used here as a rear caliper the standard front bolt is long enough to pass through the rear bridge and attach here with a simple cap-head nut. ... No drilling or cutting required!

This early 1970s bike had a simple round bridge, so the familiar old concave alloy washers were added to each side. Other old bikes sometimes had flat brake mounting plates already brazed onto the bridge... same effect.