There are a good number of folks who will feel a cavernous sorrow if the mod entails deconstructing a fully working machine. If it's already a beached carcass . . .
Any 250VDC power supply should work fine. You can get them brand new at Mouser for ~ 50 USD.
Post a schematic if possible.
http://recordist.com/ampex/apxschem.html
There's lots of interstage 'stuff' in that circuit that isn't 100% necessary for straight mic pre use. Most of the plans I've heard of involve removing these - record EQ, path switching. It will keep the signal path more pure and less noisy. The issue after that will be interfacing the output stage to a line level of the right (low) impedance. The schematic I'm looking at appears to have a transformer that will do that.
With a line out, you can already use the unit as a mic pre in stock condition. It may be acceptable as is. I enjoy the way sonic circus skirts the noise issue:
http://soniccircus.com/Ampex-350-Tub-Mic-Pre-w-VU-Vintage
I would try it first stock before jumping in with the iron. Replacing some or all of the electrolytics would be the next move -You'll probably need to do this either way. The recording EQ stacks in the grid circuit of V3 will give you pre or de emphasis and may be something the client likes - but will not be flat response. Recording at 7 1/2 ips gives a natural rise in the high freq response with a tendancy to pool in that area - probably the LO speed position.
I wouldn't do any more than what makes the client happy. Once you get to a certain point of 'cleanup' you may be very near equaling the amount of work in pulling the iron and building from scratch.