I haven't solved that problem with Elouise (16 months) yet but on Talia (2 weeks) I have been using a wool soaker, it was made by a WAHM but is sooo much thinner than my disana soaker. It is gorgeous and seems to really work. We haven't had any leaks yet - even when the nappy underneath is soaked. I have some stacinators for when she is a bit bigger. We have really got on with it!
I do use a poppolini wool wrap on Elouise, but it is too big for her in the day so we just use over bulky night nappies. It is slimmer than the disana but as we have only used it over bulky nappies - I can't comment on the clothes issue.