Pork substitute for Game Meat Pie

Duck fat.

You could use butter, of course, which would make it delicious like everything made with butter is. But duck fat has a higher melting point than butter and in that respect is more like lard. Duck fat is super delicious. Also it seems to me duck fat is more in accord with the overall ethos of a game meat pie.

You could buy plain duck fat. Or you could first have your friend over for roast duck, and you would then save the rendered fat and have her over for the game meat pie later. Do the duck in a way such that any flavor in the fat will match what you intend with the game meat pie - for example duck with Moroccan spices would be great but those spices might then crash the game meat pie party.

The problem here is that it doesn't work as you suggest,

the fat keeps the leaner game meats from drying out

What you have in your recipe is not fat, it's bacon and belly, which is fat-rich tissue. When baking, the lean meat still dries out, the bacon stays soft, and the combination feels much juicier than the pure lean meat. If you simply add some kind of rendered animal fat (or plant oil) to the pie, it won't have effect ont he lean meat, and you will end up with dried out meat swimming in fat.

So, what you actually need to do is to find bacon (or other unrendered fatty tissue products) from a species different than pigs, and use that one. It will keep the intended texture, as opposed to rendered fat.