First and foremost: IANAL - just a former software developer that has (and still does) put a lot of consideration and research time into getting into modding.

is it illegal to pay someone else to create a mod, if you then distribute it for free?

I don't think this would be illegal, and even if it was against the EULA (from the quoted section you linked it's not, as it explicitly targets the distribution & usage of mods - not development) I sincerely doubt anyone would enforce it. You're basically contracting development work, and more mods is better for the livelihood of the game.

Having a Patreon wouldn't be against the EULA or illegal either as long as they don't require contributions to access and use the mod. Banning mod developers from receiving voluntary contributions would be a bullet in the foot for mod development - you can't generally make a living off of modding but those contributions provide solid motivation for modders. I'd wager probably only 1/10 or less of the people that consume mods contribute to the people who made them, but some do.

Additionally, at a glance it looks like if you don't use the editor to create your modded content then you wouldn't be subject to the EULA at all. It would be near impossible to enforce any kind of EULA that prohibits creation of content if you're not using their software to do it.