Some great suggestions here from some evidently pretty serious acoustic guys.
I don't have a P22 or 24 but they are piezo transducers in the saddles so shouldn't be much or any different than a real acoustic with an UST.
SO...
Plugging an acoustic guitar (whether it has UST, SBT, soundhole mag pup, or multi-source system) into an electric guitar amp isn't going to get you REAL close to an acoustic guitar tone. WAY closer than an electric guitar's tone sounds to an acoustic but still not all that great. HEY...sideline and offtrack tangent here...I wonder how an SBT or 3 would sound on a solidbodied electric? Wonder if you attached some to the tremblock...?? hmmm I think I have a new project/test to conduct. And NOW, back to your regularly scheduled program...
I do a lot of solo acoustic sets on summer festival stages. I have guitars with USTs, SBTs and some with an internal condenser mic PLUS a UST or SBT...
I'm a CHEAPSKATE...well more just a matter of being broke all the time.
I went loking for a decent but affordable preamp a couple (2) years ago and I got a Fishman Platinum Pro EQ (or something like that) for like 75 bucks and they can still be found ued for that $ or maybe even a bit less. It isn't one of the $$$ modelling acoustic pres. It isn't a $$ Radial pre but it does a LOT, is small enough and sounds pretty darned good.
It has XLR and 1/4 ins and outs. Powered by battery, 9v adaptor or by the board's phantom power. You can us more than one out at a time.
It has a good EQ with parametric mids. A pretty decent notch. Phase. It even has a compression knob. Bypass. Input level and output level...
For 75 or so bucks...well I kept mine and it has served me very well time after time, gig after gig.
Definitely worth a look if you're on a budget. Does everything I need it to do and then some.
YMMV