Although the coordinating rods can be used for fine neck angle adjustments, if they are throwing the rim that far out of round, I think you need to do some coarser neck angle adjustments with shims.

Bridges come in various heights, so you can get a higher one to adjust the action, or glue shims on the bridge feet as already suggested. Bridges are pretty cheap.

As far as adjusting the distance from bridge to nut, after all else is set up properly, try this: Start with the bridge a little further from the 12th fret than the 12th fret is from the nut. Strike a harmonic at the twelfth fret on the first string, then fret the note at the same fret and listen to the difference. If the fretted note is sharper than the harmonic, move the treble side of the bridge a little farther from the nut; if flatter, move the treble side towards the nut. Repeat until the harmonic and fretted notes are the same pitch. Mark the treble position with a pencil on the head. Then do the same for the 6th string, moving the bass side of the bridge. For 5-string banjos, the bass side intonation should be set with the 4th string. The intonation of the 5th string is not as critical for most banjo players because the 5th string is rarely fretted anyway - as long is it is tuned to the correct pitch, it should be OK. But if you insist on setting that, say if you have compensated bridge, keep in mind that the 12th fret of the 5th string is really the 17th fret of the banjo.