Don't rule out heavy pellets. I have an HW97K in 0.22 caliber and mine loves H&N Baracuda Match 5.51mm 21.14g pellets at 550 fps for 14.2 ft/lbs.
I have an HW77K 0.22 caliber and that one loves H&N FTT 5.55mm 14.66 g pellets @ 690 fps for 15.5 ft/lbs.
I shoot mine up to 50 yards and while the trajectory may be more loopy with the heavier pellets, you can figure out holdover fairly easy once you find your desired pellet.
Bottom line is try various pellets of various weights and even varying head sizes. As you can see, one gun prefers a smaller head size, the other a larger one. Groups can vary within the same type of pellet just with different head sizes. Good luck!