Meat – How to bind chopped pepperoni, salami, and bacon

I have this sandwich I make that I think is pretty good, except that I have a problem with it falling apart.

Basically I take sliced salami, sliced pepperoni, (precooked) bacon, and banana peppers and throw them into a food processor to grind it up fairly ground up but not pasty.

I then put it in a skillet with some olive oil and brown/crisp it a little and then I add some red wine vinegar and black pepper to taste and set aside.

Then I take a loaf of french bread (there's this "everything" french bread at my local store that has "everything" seasoning on top of it, which I like to use, vs. plain french bread). I cut it in half lengthwise and scoop out some of the inside of the bread.

I squirt some horseradish sauce on the bottom side, then add a layer of sliced sharp chedder and pepper jack cheese. Then I add heap of the meat mix, and finally top with another layer of sliced sharp chedder and pepper jack cheese.

I then butter the skillet and press the sandwich on the skillet on each side for about a minute (like a cubano).

So this is one of my favorite sandwiches to make, and I think it's yummy! The problem is it's a little bit of a pain to eat, because there really isn't anything binding the meat together.

So I've been trying to figure out what I can do to make it not fall apart. The first thing I tried is to shred/grate the cheese and mix it in with the meat. Unfortunately, that doesn't work. I assume it's because of the olive oil and vinegar, but I haven't tried outright removing them, as it's a crucial part of the flavor I'm going for.

Next time I get a chance to make this sandwich, I was thinking maybe I would try browning the meat without adding the oil/vinegar, and instead sprinkle them on the top while building the sandwich. I figure this might help, but I'm not entirely sure it will completely help, since these meats are a bit fatty in their own right.

I was also thinking I could go the route of making it a patty (like making a hamburger patty), where I mix an egg and some breadcrumbs and cook it as a patty. I'm not so sure I really want to do that though. I'm not outright opposed to it, but I already feel like the flavor is where I want it, so I'd like to avoid throwing new flavors into the mix (though admittedly, eggs and breadcrumbs are fairly neutral).

But I'm also not sure I dig the idea of a patty for this sandwich in general. I like the mouth feels of heaping mass of chopped meat, and I actually don't mind if there's some amount of "fall apartness". I just really want to reduce it a bit somehow.

I'm certainly down for experimenting but I'm not by any means even fractionally rich, so I can only indulge in this pleasure about once a month or so, so I was hoping I could maybe see if anybody else out there might have any ideas?

If you got this far, thanks for reading my TL;DR!