This may come to late for your question of "if anyone has any ideas", BUT ..

What we've done (for as long as we've had payroll) is:
- Created a custom pay type "Stat Holiday Pay" and pay stats using that custom pay.

For stats, we export our timesheets from Connecteam (our scheduling system) for the previous 4 weeks, do a formula to divide by 20 and enter that in the custom pay.  Takes us about 10-15 minutes to do the stat holiday for our entire workforce.