I use the breakout board to power the motherboard, not the pico's supply. I have a special cable with a 6 pin that plugs into the breakout board and the other end is an 8 pin which plugs into the motherboard (8 pin cpu power connector). There a two wires that branch out from the 8 pin to attach the 12v dc barrel plug from the Pico. This take the load of the CPU off the Pico and puts in onto the Server supply. Also if you are running OS from flash drive, the breakout cable of the Pico is not even needed.
You can also just use a 6pin to 8 pin cable to plug from breakout board into the motherboard (which you may be doing already). Good luck.
I too as well, use this type of setup, mobo 12v is powered right off the breakout board, theres a pigtail coming off that 12v with a barrel jack for the pico psu that way the pico isn't running full load, more like half load, I also custom make my own 12v cables with a pigtail for the pico