If it's separate diodes, 1n5404's do nicely in the 31-R for the B+. It's very much like the 59T/59A combo just stuffed into one chassis. If it's a bridge, use what's used in the 400-400c-800c for the B+. 4A is plenty enough, tho a bit of overkill. For the Heaters either a 2A bridge or 4 1n4004 in a full wave configuration should be fine.
Stay with original cap values, but up the voltages by 1 step. ie: 50v to 63v, 16V to 25V or 35V. Upping capacitance in these doesn't do anything but make your wallet squeal a bit more. With the exception of C63 & C64. Bump them up to 2200uf 63V (originals are 35v to 50V) any more than that and diminishing returns.
Usually it's the FM section that's quiet and AM that has noise, hash, etc. at one end or the other. It could be an artifact of the DBT(not enough B+ for the front end) or an alignment issue, or any number of things. Eliminate all the RFI in the area (switching supplies, Florescent lamps, etc.). A transistor might be going bad too.
Sounds like a lost ground on the phono circuit. Start at the tonearm/headshell. DUAL 10xx series are notorious for that. DeOxit and an eraser will clean the contacts (don't forget those in the carrier for the headshell).
Clean the heads, then de-magnitize them. Then play again. If no joy, Swap the outputs on the R2R and replay. If it's in the tapedeck, the lack of sound will swap sides.