My k24 burned a lot as well, stuck rings. What I did was a piston soak with Berryman's B12 Chemtool, then many runs of Gumout Multisystem Tune Up, Rislone Engine Treatment 32oz bottles, and then HPL EC30. I also used Motul XClean oil for 2 5k oil changes. All this took place over 2 years and my consumption is about a cup per 5k oil change now.
What I would do if I was you is start with a long, >12 hr, piston soak with Berryman's then run nothing but the new Valvoline Restore and Protect 5w30. At the end of the oil changes if you wanted to speed things up a bit you could do a flush with BG EPR. Valvoline was not out yet and I would run it exclusively unless you wanted to pony up for a HPL passenger car oil.
Good luck just be patient