I think a mild sensor lift would fix the pogo’ing that happens when going over speed bumps.
And, barring the availability of a slightly stiffer front coil, that may be the only solution…ideally I’d like a set of terrain tamers for the rear and for the front.
I think you had a list of spring rates for the various front coils available to us.
Did you ever figure out what the front coil’s spring rate was?
Haven't been able to find data on the front rates.
With AHC, the modification strategy is different from static suspensions. Going straight to heavier coils may not be the right solution.
I have run AHC bone stock with 2k payload and it worked great there except the system wouldn't go into high anymore, which is expected per the manual. I've incrementally upgraded with front spacer, rear spacers, bigger rear spacers, sensor lift, and now have a variable rate rear setup with airbags. The system is pretty flexible and has worked well for me in the stages of upgrade.
I'd start with a minor sensor lift and see if that changes any impressions. Easy, no cost change. And easy to revert. Take each sensor, critically mark current position, then shift by ~1/4". You'll want to look in this thread as I forget which way to shift the front axle sensor vs the rear axle sensors as one of them is in reverse

LX570 AHC height modifications (lift it!)

It's very possible that you need replacement globes per @tbisaacs . It may be one of them is weak and pegging out lending to the pogo'ing. Why it doesn't seemingly happen in high is why I'm scratching my head, but there's merits to his suggestion. That incremental sensor lift may tell us more?