My understanding is that riot and the slumber counters are both replacement effects and I can choose the order to apply them. So if I choose to apply riot first, then Arixmethes can enter with a +1/+1 counter, even though it ultimately ETBs as a land, not a creature. Is this correct?
Edit: I asked a judge and they said that riot always applies to Arixmethes, regardless of the order. So I guess that settles that.