I would vote for building/sourcing a linear 12v power supply which would not have any power line induced or more importantly RF emitted noise and using that as your central 12v power distribution source. Probably lots of candidates out the on fleaBay to choose from as a building block. You could use a small car battery charger, whack in a full-wave bridge, add some 10Kuf filter caps, regulate it with an LM-338K (or a low dropout voltage LM1084IT-ADJ ) and there's a solution for a pretty cheap and plenty of +12vDC power supply for your needs (and output voltage adjustable with a pot, if you wanted). Total cost for the mod parts mentioned is about $10 or so.
http://www.ebay.com/itm/Schumacher-8..._Tools&vxp=mtr
Tom (PK)