I'm pretty sure someone already mentioned this before, (I'm too lazy to go and look) but there could be serious problems when using an Op-Amp with "normal" offset.
In simulation I was having problems when the reference voltage was really low, and I think this was why, because I was just using the most generic OP-Amp I could find. If we haven't done so already, (can't remember) It might be worth it to invest in low offset + rail-to-rail type Op-Amps. A low offset can't possibly have negative side effects as far as I know, so there is no reason not to do this other than to save like $5. And a rail-to-rail Op-Amp lowers the minimum current we can make the system draw. Also good.
Here is a simulation with a more or less "normal" Op-Amp. The green line is current, the blue is our control voltage. Notice that even when the control is telling it to, the current can't go below ~5 Amps. Not good at all.
And here is the same simulation, the same control ramp, this time with a better Op-Amp. Note that you can't even see the control voltage this time because it exactly follows the current. Which is what we want.
The more I think about it, the more I think we have gone over all this already. If so, disregard this post.