The 4.25 guns run well and it sounds like Springfield has sorted out every gun that has been sent in for repairs. Also, some issues are addressed by simply using higher quality magazines.
As mentioned, you can very easily replace the ignition parts and have "better" internals than a staccato for much less.
Plenty of people who shot both, actually prefer the prodigy.
It's a bit amusing to see people shit on the prodigy for sometimes needing minor work (usually better mags or different recoil spring), considering it's a $1250 optics ready 2011. STI was selling a $2000 (pre-covid money, back when the dollar was worth something) 2011 that wasn't optic ready and typically needed work to run.
I'm not a Springfield fan, or a staccato hater. I have no dog in this fight. Plenty of people have done what you are asking, it's entirely reasonable to expect the prodigy to run well with minor work (or in most cases, no work). You should go to pistol oriented forums and learn there, not here.