If you want it cheap - this project is fully open source - one can make the board themselves, might be possible even order it assembled in larger quantities from PCBWay or JLCPCB.
I'd probably say suck it up and solder the QFN directly if you need all the GPIO in minimal space, though.
I've had stuff that wanted 3-5 pins, or maybe 10 pins. I've had stuff that wanted 100's of pins. I can't think of anything that wanted, specifically, between 27 and 30 inclusive.
Does the Pico really fail to bring out 4 of them anyway? That is kind of surprising. I know that it uses one of the ADC's for battery monitoring, leaving just 3, but maybe you can get it back by cutting a trace or something.
Is it practical and useful to connect 20+ of the pins to PIO ports? The PIO's are very limited.
This brings out 20 and has castellated pads: https://www.adafruit.com/product/5302
This is bigger but fancier, has a lipo charger and other stuff. I think it brings out all available pins, though the # mentioned is 21. More of an SBC than a solder-down, I guess. I have one (old version) but am trying to figure out where I left it: https://www.adafruit.com/product/5302