you could use a Mayhem to force your opponent to get some souls out.
I was thinking about it but that seems very hit/miss and it might make ME draw ls as well.
true, but you could put it in there and judge if you want to use it. if you already have a couple of lost souls and no sites, then drop a Mayhem after they draw. there are plenty of other uses for it as well. I'd also use a thorns lost soul to prevent them from SoG a shuffler.