I set up Recalbox recently, but haven’t got as far as testing Picade with it.
If it has trouble with some of the keycodes that the Picade PCB uses, you could update the firmware (of Picade) and try adding your own custom keybindings to see if that helps.
The latest firmware and the updater tool is available here: https://github.com/pimoroni/Picade-Sketch/tree/master/update
You can then experiment with custom bindings, emulating a gamepad, etc.
There’s a guide to accomplishing that here: New 2.x Configurable Keyboard/Gamepad Firmware
I’d try prodding Recalbox, or using RetroPie first, though, since that may be less hassle.