There are no rules for this.
The rules for costs are basically a function of what economists call marginal cost—what it costs you to make one more unit of something once you’re all set up and have already started producing. For a spellcaster, the marginal cost is their time and the spell slot, as well as any expensive material components of the spell. These things are all factored into the hiring rules (actually, the spellcaster’s time doesn’t factor in—there is no modifier for spells with long casting time).
What isn’t factored in, at least not explicitly, is the time and expense of getting to the point where the spellcaster could even offer this service—the cost of becoming a spellcaster, and of achieving greater levels and thus having higher-level spells available. And that’s exactly the place where we would expect to find something like feat selection factored in. And it simply isn’t.
Feats are preposterously valuable. D&D 3.5e’s Arms & Equipment Guide suggested 10,000 gp was a decent starting point for valuing a feat, but many DMs found that number dubious—and many players found that number quite attractive, and pushed their DMs to accept it.
But you aren’t asking a spellcaster to select a certain feat for you. You are finding a spellcaster who already has that feat to use it. And that costs them nothing. On the other hand, just because it doesn’t them something doesn’t mean it isn’t more valuable—it clearly is, you chased them down specifically for that feat. That means it has value to you, and the character in question knows it and thus expects that they could or should be able to convince you to pay more for their work. Most merchants are going to do that when they think they can.
So it’s going to be up to your GM. And, in fact, it may very well be something that is up to your negotiating skills, in-character—a GM may very well expect you to use your skills and abilities to find such a spellcaster, and then to negotiate with them. Even if it’s part of your backstory, you might negotiate with the GM by negotiating with the spellcaster, in character, as your character.