I'm not vegan, but I've acidified with DVI culture before. You couldn't do that and use DVI culture because it has milk and whey products in it. You'd need to figure out a way to get vegan culture, and the only one I know of is the acidophilus. Although, I think there are other probiotics out there, and kefirs. You can try those. You can also reculture multiple generations from DVI and keep your own strain that has origins in non-vegan sources, but through successive generations, that should go away.
For an aged cheese, you need to create a milk profile that is high in fats. You couldn't easily do a rice milk cheese, for example, and I'm dubious about an almond milk cheese. You could use brazil nuts, hemp, macadamia, perhaps peanuts, hazelnuts (you should try making an aged chocolate hazelnut cheese... it's great), cashews, etc.
If you want a real, sliceable, hard cheese texture, you cannot do it using only the milk. You will need to use additives to stabilize, and emulsifiers to give it an even paste. Like Daiya does.
Using rennet to coagulate nut milk doesn't work. Nut milks have very different proteins, and multiple fraction types of them, which are comparable to the caseins in milk, but the caseins in milk are in micelles, whereas the proteins in nut milk are just proteins. So you would need another enzyme that works on those specific proteins. You may want to try some vegetable enzymes, such as papain. You can also try to solidify with salts, like you would for tofu. Calcium, magnesium salts work.
If you use an acid coagulation, it will give you a crumblier cheese. Sort of like a cream cheese that's solid and slices after aging and losing enough water.
Also, if you want something to taste like a cheddar, you can't get there with nut milk. You can get something that has aged cheese notes, but it will be different. You'll probably like it, but if you're hoping to replicate an artisan cheddar, I don't think it's possible.