Okay, I agree that the universe may not be Turing-computable, since we don't know the laws of physics. Indeed, it almost certainly isn't, since Turing machines are discrete and the universe is continuous -- there are integrals, for instance, that have no closed-form, but are physically present in our universe. However, I have no particularly good reason to believe that infinite precision is actually necessary in order to accurately simulate the human brain, since we can get arbitrarily close to an exact simulation of, say, Newtonian physics, or quantum physics minus gravity, using existing computers -- by "arbitrarily close," I mean that for any desired threshold of error, there exists some discretization constant for which the simulation will remain within that error threshold.

Sure, maybe there are more laws of the universe we don't know and those turn out to be necessary for the human brain to work. But it seems quite unlikely, as we already have a working reductionist model of the brain -- it seems like we understand how all the component parts, like neurons and such, work, and we can even model how complex assemblages of neurons can compute interesting things. Like we've trained actual rat neurons to play Doom for some ungodly reason, and they obey according to how our models predict. Yeah, maybe there's some critical missing law of physics, but the current model we have seems sufficient so far as we can tell in order to model the brain.

constantly interacting with the rest of the physical world

I feel like the rest of the world shouldn't actually matter for the purposes of free will. I mean, yes, obviously our free will responds to the environment. But if the environment disappeared, our free will shouldn't disappear along with it. In other words, the free will should be either entirely located in the mind, or if you're not a compatabilist/materialist, it's located in the mind plus some other metaphysical component. So, I don't agree that it requires simulating the whole universe in order to simulate a free will (though I do agree that you can't simulate an actual mind in the real world unless you can simulate all its inputs, e.g. placing the mind in some kind of completely walled-off sensory deprivation environment that has within-epsilon-of-zero interaction with the outside world. Obviously, it's not very practical, but for a thought experiment about free will I don't think this detail really matters.)