Don't worry, Leylandii does not grow back from old wood, this is why you see so many leylandii that have died due to them being allowed to get too big before cutting back.
It's pointless trying to kill the stumps, if they are going to die anyway.
What I would do is leave the stumps long, approx 3-4 foot high, then get them winched out, if your in no hurry, they will come out easier, the longer they are left.
Otherwise, hire a stump grinder, to grind them out, if the stumps are low.