[NFP] Trying to apply Babylon's free buildings effect to unique districts

[chiphead]

I am attempting to allow a modded civ with unique districts to have Babylon's "free cheapest building in first district" trait. The effect works fine if I revert to default districts, but not on a unique district, whether newly created or copied from an existing civ (Lavra, Suguba, etc.). Is the list of districts to which the effect applies modifiable somehow?

The effect in question is

<EffectType>EFFECT_ADJUST_PLAYER_FREE_BUILDING_WHEN_SPECIALTY_DISTRICT_CONSTRUCTED</EffectType>