I've been working with a lot of 70's -80's 2203 variations and, since you're using the LO input, it's losing a bit. I'd redo the LO jack circuit insertion like this. (And, doing this basically makes it more like a 2203 but, I suppose Sovtek couldn't copy it "exactly", lol). And, I'm also assuming your first two stages are the same as the schematic you shared.
1 - remove the 1M resistor at the V1.1 output.
2 - remove the 1M grid leak at the V1.2 input grid.
3 - replace the 0.047 cap at the V1.2 input with a 33K resistor (this completes the grid leak bias circuit thru the 1M volume pot...i.e. why we can remove that 1M)
4 - Now THIS depends on how all is wired and the ease of changing it up. You really want that treble peaker (i.e. 470K||470pf) between the LO jack and the top of the Volume pot. That'll add 50% more resistance and you gain the effectiveness of the treble peaker. So, if possible reroute the treble peaker to the tip of J2. And, the J2 switch would then get connected to that V1.1 0.047uF cap of the plate. If you can't easily rewire the current treble peaker then either remove it and replace with a shorting wire (then add it between the J2 switch lug and wire)...or...alternatively you can leave it...but short it and insert a fresh 470pF||470K pair between the J2 tip and the wire. Either of those effectively does what we want to do...that is to insert the treble peaker on the J2 TIP to get a better loading/frequency control for that input (i.e. similar to a 2203).
My gut says Sovtek did that to further remove the comparison to M@rshall and because not many people use that jack.
5 - Last, but not least, insert a 100pF silver mica between the Volume wiper and the top terminal to maintain a 'bright cap', but make it (my opinion) more suitable for preserving that top end sparkle.
If your Sovtek looks like some of the chassis photos I saw, it should be easily doable...? And, vs. 0.022 (ala 2203-style), I'd leave the 0.047's for now til you've determined that the changes above either resolve it or you're maybe now too strong in the lower freq. range than desired.
One last comment, you mentioned a Big Muff in there. Is that pedal always buffering or does it provide true bypass? And, when you're referring to this MIG being 'too bright'...are you comparing it with a straight (pedal-less) plug-in scenario as anything pedal(s) in between can change the reasons why the comparison is not quite the same.
Overall, you're still a far cry from a 70's 2203 with those changes, but it's a start that (I believe) will start heading you in the direction you want with minimal effort to start with. The circuit I really like using is the 1978 Master Vol. MkII 2203U ...search and you'll find it. That production year has gobs of beautiful tone I love.
Bottom line...have fun with it!
Brad