A good first step would be to post an inside chassis circuit board view of your amp, a picture is sure worth a thousand words, especially here.

If you're not getting ample volume, when neither the Overdrive or Boost foot switch is engaged, something is definitely up. A 20w amp isn't going to get crazy headroom, but it should have a substantial amount of dB's, just under as much as any other high wattage design.

Yes definitely solder the adapter to the board, but either drop a dab of silicone &/or zip tie the Relay to the socket so that it firmly sits in the socket.

Those are adapter's for the relays. Sometimes Relays fail and it's nice to have a socket there to just pull them out and replace them. Cut the leads on the adapter's that aren't being used and they'll fit in the PCB. Add a little dab of Rtv (Silicone) or Zip tie them so that they don't move or fall out.

I like to wire up a 250pF mica cap on one side of a relay, to be switched in series with the treble cap (like a mid boost without the 3.9M Resistor to ground. I add the 100k to the center of the treble pot, to be switched to the center lug of the bass pot. Then put a 120pF bright cap on the other side of the switch controlling the relay. This is kind of a Strat/humbucker switch. It lessons the lows, without rolling high end off and increases the high end content all at the same time. It's a Mid shift, Bright increase, and Bass Cut in one control. It could easily be done with a 3pdt mini toggle as well.

Also Another good mod is to Have the regular Preamp Boost and a Full tonestack lift both on relays, I wire the Bass pots's 10k to ground to the Mid controls Ground, then lift the ground with a relay. If you wire the tonestack lift backwards to the regular preamp boost, you'll get 2 different distinct boost options. Add a Trim pot to the Tonestack ground lift and you have a variable preamp boost too.

That combination of speakers will be fine with a 20w Output section. You don't have to worry about over compensating with speakers with a low powered amp. You would however have an issue if it were a high powered amp 100w or more. You'll get more clean headroom with that speaker configuration. I also highly suggest re-wiring the cab in Parallel (assuming both speakers are 8ohm's) and using it as a 4ohm cab instead. The 4ohm Output Impedance tap will have a tinge more high frequency content because of it's relationship with the global negative feedback in the presence circuit. That in combination with flipping the phase on the speaker cable are some easy DIY mods that will only help with great articulating in individual notes, feedback, as well as sustain.

You would be better off punching the chassis between the OD and PI preamp tube and doing it PTP. Take your B+ from the first Screen Node, drop it, and then add your 2 Loop B+ stages (Plate and Cathode follower).

Having the Tube loop will definitely make things more grab and go. Just be aware of the right lead dress.

Not a ceriatone, but this is how I do it in my amps: