You might want to turn down the gain on your keyboard, it sounds like you're shouting...
I like to run my piezo through an acoustic simulator and EQ, and then clean to the PA/acoustic amp. Reverb just muddies it up. Now, if I run the piezo or regular pups into the other loop/line with some dirt and other effects, then reverb and delay can sound awesome - but then I'm using the piezo to fill out the signal, not for its overall acoustic-like properties.
I would not suggest buying a pedal specifically for stereo until you really know what you want/need. Heck, it might be cheaper to buy two separate pedals, one for piezo one for elec pups, so you can tweak the delay/reverb specific for each signal. So just get a mono delay/reverb to play with at first. I would suggest a delay first (unless you can find a good combo pedal), and then turn down the reverb on the amp until you don't quite notice it. But that's up to you.
You can do one of two things, IMHO, depending on your personality and level of risk aversion (and what you consider a risk):
1. Pick up a cheap but competent delay/reverb clone (Behringer has one, Joyo has a couple), see how it sounds for both piezo and electric pups. If you hate it for either, even with the effect mixed in really low, then you can flip them on eBay or Craigslist or whatever - not too much invested (especially compared to the cost of your P22!)
2. Analyze and investigate the pedals your guitar heroes use, and how they use them. Figure out one or two that you absolutely think you can't do without to capture their sound. Buy either that exact same pedal, or another similar pedal that is pretty darned close. (e.g. maybe you want the Gilmour sound, but he has used so many delays over the years I doubt anyone could say there is only one pedal to capture "his sound", so any of the analog/digital delays might be enough to start with - but there are pedals that can capture his sound from specific eras, like the Catalinbread Echorec, supposedly - I intend to buy one of those soon...)
Anyway, good luck! And please turn off the CAPS LOCK...