Maybe an aged cheddar? I've seen apple pie offered with a wedge of cheddar, and have seen recipes for shredded cheddar in pie crust for apple pie. One of my favorite grilled sandwiches is deli roast beef, aged cheddar and chutney. I think cheddar pairs well with sweet.

Your burger sounds good! With pork in the mix, though, you must have to cook them well.

I'd be tempted to try a soft cheese like cambozola but that would add a flavor (and heaviness) all its own. You didn't list provalone; pretty neutral and goes well with beef.

Feel like sharing your creation in more detail?

Or brie. For some reason, that idea is jumping out at me.

My thought was cheddar too. Not a sharp one.

Jarlsberg, Gruyère, Lancashire cheddar, Edam. If you have access to Costco, they usually have a good selection of cheeses.

Apologies, I had meant to post the full recipe in the OP, but I was not home at the time and for some reason FB, where I had the recipe posted for family in the north, wasn't being very responsive. So here's the recipe as I have it posted for them. (Disclaimer: I'm no cook, I just got lucky with this one.)

"1.4 lbs Lean Beef (10% fat)
1.1 lbs Ground Pork
5/8 cup brown sugar
2 tbsp A1 sauce
Add above ingredients to a large bowl and knead repeatedly until everything is thoroughly mixed. Feel for a hard lumps in the mixture as this is where the brown sugar has balled up and they need to be crushed or it could lead to a bad surprise later. I kneaded for approx 5 minutes.
Separate into patties. Using a patty guide, I made 7 - 1/4 lb burgers and 1 - 1/3 lb burger. Lightly sprinkle both sides of the patties with a half-pinch of sea salt and 3 grinds from a pepper grinder. Set the plate aside.
Now take 6-7 Sweet Gerkins/Pickles and slice them into thin spears. Place them in a small bowl or dish. These will be used after the burgers are done.
Cover one half of your grill in foil and leave the grate open on the other side. Preheat to approx. 300F for about 10 minutes. Grab the patties and your favorite bottle of beer. Place each patty on the foil side and cook them for about 3 minutes per side, 3 1/2 for more done burgers. Then transfer the patties to the unfoiled side and grill for about 30 seconds on each side to give your grill marks and add _just_ enough char flavor.
Remove and serve. You are welcome to add cheese, but it is my experience and humble opinion that cheese will detract from the sweetness of the burger. When building the burgers, add 3 to 4 of the thin sweet gerkin spears to the top. Add any other condiments that you might desire, but bear in mind that this is a sweet-tasting burger."

For the longest time I just eyeballed everything, but when I moved from Michigan to Florida some of my Michigander family wanted the recipe, through trial and error I finally came up with the above measures. Cooking for three minutes will result in browned pork but the beef will stil be a tad pink. I don't know if this is due to the difference between pork and beef or a result of using the brown sugar. A word of caution though: With the brown sugar added you will really want to keep an eye on the burgers beyond 3 1/2 minutes per side, the brown sugar can quickly take the burgers from done to burned.

Enjoy.