a few options for you, most of which are speedy on account of the fact that you will need to cut lots of rivets! A saw is too slow I reckon and will likely damage the brigandine.
These bolt cutters are basically side/wire cutters on steroids. They should go through a 3mm nail ok, if not then see if they do a larger size. Might be worth heating the nails with a torch or putting them in a fire just to anneal them, often nails are cold drawn and so are harder (they have work hardened) than you want to cut through by hand
Use small bench shears like
these to cut the nails off at an angle before you start, then you have pointy rivets of the right size to start with
Dremel with cut off disc, even a battery powered option.
when I had a load of short rivets to make of the same length, I made up a simple bolster from a bit of steel plate of the thickness that the rivet needed to be. a length of stock the correct size was placed into the hole (with the bolster laying on my anvil) and the head formed with a top tool. Those were all 1/4" diameter with dome heads, so was all done hot, but I think it would be fairly simple to make a tool up to make a short pointed (though a dull point)rivet in 3mm mild and it would work cold. Then if you use a chopsaw or bench shears to cut the lengths of rivet, you drop one in and twot it to spread the head out, then turn over and tap the piece free.
Or of course the easiest might be to ask about amongst other re-enactors who make that sort of thing, somebody will have found a solution by now!