I'd suggest power supply mods before anything else, power supplies are almost always the lowest hanging fruit.
I totally agree with the first part: for Line Level, the power supply is extremely important. Anything occurring at Line Level output will subsequently be amplified,so the cleaner it sounds here the better. It is helpful here to think of what you are hearing as a modulation of the power supply, so that you know it's super important and audible, and it's no surprise you should spend a lot of time optimising this.
Here are a few things you could potentially try, but if you're not too comfortable, ask someone to help as mistakes made in this area can be detrimental to you or the gear or both:
(a) Replace the diodes in the rectifier by Schottkys
(b) Twist the wires AC-side before and after the Toroid. Someone like Ric Shultz may advise some additional mods here, like for how to make a physical mod to the toroid (have to be careful of not shorting the core here)
(b) Add a snubber on the Toroid secondary(ies)
(c) Examine the filter post-Toroid and make it a CLC, a i.e. use a Choke there
I can't say from here how the regulation section is, but there should be one (probably the chip on heatsink and surrounding area on the bottom right). You could potentially replace the man chip there, but the best thing to use in this area is a shunt regulator or a super regulator if it hasn't been installed. You could build or get a crop-in replacement or mod this area if you get schematics or can analyse it.
Now, this doesn't mean you cannot get further SQ with other parts, like with changing the capacitors and so on.