The notion behind a separate power supply is to put distance between the power transformer and the rest of the circuit. That assumes that the power transformer has a magnetic field that needs to be kept away from the circuit. As PB implies, separate boxes and umbilicals carrying high voltage are a recipe for a fatigue induced disaster. Our newer transformers are designed to work fine close to the circuit and we take pains to mount them in a position that gives the lowest possible noise. That said, the Afterglow could benefit from playing around with the relative position of the power transformer, choke and outout transformer as our skills were not as well developed when we did that circuit almost 30 years ago.
Looks to me that this separate power supply configuration creates a lack of continuity in the chassis ground plane. If the inductors are mounted such that they electrically isolated from the chassis to avoid the generation of eddy currents in the chassis and safety ground drain wires run from the inductors to a common safety ground (as we do) and, assuming that ground point for these drain wires to be on the power supply part of the chassis plane, you now have a second (amp) plane that is floating with respect to your power supply ground plane and inductors - a potential source of noise. The solution to that would be to connect the power supply chassis and the amp chassis planes together. Easiest way to do that is make one chassis rather than two.
My thought is to make one big chassis plate and put more energy into experimenting with the relative positions of all the inductors on a breadboarded circuit, keeping in mind the notion that rotating each inductors core 90 degrees relative to the other inductors and keeping those orientations centered on each inductor's axis usually minimizes magnetic coupling. We have found that this is an area where moving the iron and looking at the noise floor on a scope often shows the most optimal position and that sometimes the best spot doesn't perfectly match the theory.