+1 on checking the bridge carefully for contact and verifying the seating of the A string in the nut with proper break angle. It's not unreasonable to try a third set of strings. GHS Pressurewounds perhaps. Rotos are notorious for dead strings, don't know about DRs.
Action height? Measure at the 1st and 17th fret on each string and compare with specs (0.022" and 7/64" bass side to 5/64" treble side is typical IIRC).
You could try slightly adjusting pickup height too. Certain Fender Jazz pickups have raised A poles to get the magnets closer to the string, as on my FSR. DiMarzios have individually adjustable pole pieces.
This kind of thing seems to require some voodoo to get it sorted.