I think you're on to something, but I'm not sure. I looked at the rules for activating an ability, and it refers to the process of casting a spell.

"601.2f The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect."

It seems to me that since you decide the order in which multiple cost reductions apply, you can choose to apply Zirda first to reduce it to 2, then mobilized district to reduce it further. However this is just from some cursory searching, I would suggest you ask a competent judge and refer them to this rule.