Here's the central problem: Neither of you have any idea about how to plan a wedding. You're both insane.
The ideal wedding you're describing? WAY MORE than 5k. You're in for seven to ten conservatively. And I say this as someone planning a wedding as we speak. I have a 350 guest list and a 20k budget. What you're talking about is way, way more expensive than you think it is.
Here's is how you plan a wedding
Take this list. Now rank every item in terms of importance separately.
Then go hit your head against the wall until you fall unconscious because you realize you have not thought about half of this bullshit.
Just kidding.
Straight talk: you're going to have a big wedding. There's no talking him down. It is happening. Get over it.
Straight talk: You're not getting married in a church. You're not budging on that. It's not happening. Get over it.
Straight talk: Expect to pay at least ten grand. That's just what it costs these days. Sorry. But take comfort in the fact that inviting more people means you get more envelopes in cash, so it might actually save you money compared to your plan.
The bigger point: weddings are a nightmare. You both need to abandon the idea that this is going to go well. The day itself will be AMAZING. Planning it is a shit show. He's entitled to invite his family and friends and you're being a jerk about it. I don't care that you hate crowds, you're be way, way, way too busy to have more than ten seconds of conversation anyway. You won't notice. And his church thing is just bullshit. Find another option and put your foot down. And then realize that there are a thousand other details that are going to make you crazy and accept it as part and parcel.
That, or elope.
And, honey, you're going to spend money. Obscene amounts. The sooner you come to terms with that, hyperventilate, and resign yourself to the reality, the easier it would be.
That, or elope.
If I were your wedding planner here's what I'd tell you to do.
Hire a photographer for three-four hours to cover the ceremony, get a couple of family shots, and then some photos of you two. It saves money. Find someone you like with a big back yard, do the ceremony and reception there, and then rent tables, chairs, and sound equipment from a party rental company. Get something cheap but tasty catered (Grocery stores do this, as does Panera and Chipotle, chinese places, Thai, Indian, BBQ, food trucks, there are options). That keeps the cost down. It also tastes better than the $30/plate you'd get at the restaurant. Get a spotify playlist so people can dance but you save the cost of a DJ. You won't notice the crowds since you'll be too busy, but keep a friend close so you can duck out whenever you need to. Buy keg beer and wine by the case to keep the liquor costs down.
Even with, say, 140 people you're in and out for about what you'd pay for the restaurant. It takes care of the money thing. It solves the church problem. It fixes the guest list because the price per person goes way, way down by the DIY food and liquor. You're still getting out of there for around 7-10k and you solve basically all the complaints.