A catwhispering friend of mine always says that the first thing to do with litterbox problems is to have enough (clean) boxes around the house, typically the number of cats plus one, so 5 for you, Treegod. That way there's always a "free" box available. Place them in a few different area's around the house. If things get going the right way again, you can try to reduce the number of litterboxes.
A second thing is size: as Aphritha says, the size of the box matters. For my 4 kg cats I use the size box for maincoons. They have a hell of a time playing in it, trying to dig to Australia and sometimes using the same box together at the same time (like all girls seem to do, on a sidenote: the girl's boxes are in our mudroom where there's also the door to one of our toilets. My guy always cracks up over the fact that whenever I go to the loo there, the girls follow me and go to their boxes at the same time.).
Cats can also get onto the edge if: 1 they don't like the litter used (changed it recently, or is the brand the same but "new and improved"? Do you use enough? They really like to dig deep often); 2 the litterbox isn't clean enough (selfexplanatory) 3 they are straining to push it out (perching on the edge can give a bit of leverage there), so check the consistency of the poo, if it's dry and hard, maybe it can be solved with a dietary change. If it's to soft, also. Since you say it leaves a mark, that could be the problem. You're looking for a nice smooth cigarshape

Also make sure they drink enough water. 4 It can also be another medical or cat-geriatric problem: some cats get a bit funny with age, others lose control (although that's mostly pee first, poo later). Deworming might help, as might defleaing.
If other issues are resolved and/or ruled out, a practical solution might be using a closed/high litterbox (that's really big enough). There are folks using certain kind of Ikea storagebins for litterboxes, google around a bit and you'll find a lot of made to measure options that don't look as ghastly as some litterboxes do.