Spells that allow you to take the city using influence should not be affected by this, since they aren't really able to be captured that way until mid to late game, or at least I have never had the influence to do it until then.
You're doing it wrong. You should try a "Heroic" + "Wanderlust" + "Betrayers" combo. It's ridiculously overpowered in more than one way, but in this particular case I'm talking about:
1. Spend Gildar to buy quests maps
2. Use quest maps to generate quests
3. Solve quests to get influence
4. Use influence to have cities join your side
5. Use cities to generate more Gildar
6. Back to 1.
For bonus points, pick 'Men' as your race, and make solving quests trivial by stacking your sovereign with as many henchmen as you can.
Each henchman should start with "Bard", "Shieldwall" and "Potential", wield a lightning hammer, and prioritize the "Potential", "Trainer", and "Tactician" lines. Those stack, and henchmen do not reduce the gained XP. So by turn 80 you see henchmen with levels in the mid 30s, and a stack of those can kill three ashwake dragons before they can act ONCE.
By the way, you can do the exact same thing with scions, but you will have to spend twice the influence on them.
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Ah well, I just realized that you cannot stack all of these anymore. Good job, devs, that one needed to die! Just modify your strategy to get quest maps from Altar. Make them sure you scout them early and keep them alive.