There's been some good advice so far, I'm impressed!
Here's my 0.02p...
PSU
I think the greatest problem may well be the unregulated DC you're feeding to the Prefix.
A better solution
may be to feed
AC to the Prefix box and put the rectifiers / smoothing in there.
Since this isn't practical some pre-regulation would be worthwhile, I feel. The problem is the AC from the transformer will be nominally a sine wave - with care in cabling / wiring the radiated field from this can be controlled quite readily, but the rectified / smoothed DC you are feeding, whilst it looks 'cleaner' will have ripple superimposed on the DC and due to the switching action of the rectifier diodes there will be greater high frequency content, ready to couple into the high-gain, easily upset, phono stage.
The only real wiring mod I'd make in this box is to reduce the length of the two green wires from the RHS of the bridge ass'y, bend these a little sharper and reduce the length between these and the pink wires at the other side.
Nothing major
DIY-fix
The unscreened input wiring rings alarm bells here, adding some screened, low capacitance cable from BNC - board or, even a lightly twisted pair would work better, from BNC - board.
If it were possible I would have put both phono board side-by-side and put the TPR's the other end of the box, assuming a DC regulated feed.
Further to the internal wiring you have both input signal wiring and o/p signal wiring floating in space.
Are there any 0V connections to the BNC's, I can't see them in the pic?
The input signal from the cartridge is created in reference to the -ve of the cartridge, therefore all wiring at this point needs to be reference to the cartridge -ve.
Simply put this means two closely-spaced parallel conductors running from BNC input to the board (co-ax / twisted pair/ cable tied harness).
The same is true for the PSU to the boards, so again the PSU wiring from the board to the TPR's should consist of two closely spaced parallel conductors (as you've done). This also applies to the input to the TPR's. Two paralleled pairs should run from DIN to TPR boards (again this looks good as you've done it).
Now what about the o/p?
The phono board produces an output that's in reference to its 0V, but if we run another 0V from board - DIN we create an earth loop - you already have a 0V running from DIN - TPR - Phono stage, so the best solution is probably to run the more robust, low impedance output signal in a single wire, but route it alongside the existing 0V wiring from the PSU.
A diagram would be easier, if I get chance I'll try and scribble something, but don't hold your breath
You may also wish to add an output resistor in series with the phono board output (at the DIN socket, preferably) to decouple the effects of cable capacitance from the phono stage, which may cause instability. Try 10-100R, this adds isolation so that the phono stage doesn't see any capacitance from the subsequent wiring, that could impact it's stability.
Hope that helps.
Andy.