Might be a good idea to set your campaigns during the 1st Succession War. The former Hegemony worlds were pretty much a free-for-all in the early stages, and everybody fought everybody else.
If you want to avoid that, things get a bit harder. It was pretty rare for Houses to fight against folks they didn't share a border with. For Steiner/Liao or Davion/Marik conflicts, you could look to the 4th Succession War and the fighting that claimed the worlds to form the Sarna March, or Operation Guerrero, when said area collapsed into the Chaos March. Come to think of it, the 4th War gives you a good backdrop for just about everything. Kurita/Liao and Kurita/Marik is a bit harder, but you could frame them as deniable raids by "pirates" during the time leading up to the forming of the Concord of Kapteyn, aimed at destabilizing one party to give another an edge in the negotiations.