I'm pretty sure peat takes care of both GH and KH, but can't really find anything to back that up outside of forum posts in google...
I experimented with peat a little, and in a 10 gallon tank I got it from 7.6 to 7.2 using a golfball sized amount of peat in the filter over the course of two days. So in filter it won't radically swing out of control if you're just using tiny amounts at a time. Filtering water through a huge pile of peat outside of the tank did reach the lowest end of my test kit, 6.2. If you filter through it outside the tank you can slowly add the concentrated peat "juice" to the tank a little bit at a time and fine tune the pH that way. But it's a lot more work, especially if it's a big tank.
I was also thinking of rigging up a large coffee machine from the thrift store to do this for me, but my rams don't seem to mind my 7.6 water anyways so I just gave up on that.
Good luck, I hope something works out for you