Aiming at the extreme left or right of target might get you there. If that doesn’t work aim at the tippy top of target or below bottom of target. Or one shot at all the extremes, for an awesomely centered sub-MOA group at distances out to 1000 yards. Give it a try and post up.
Move the bullseye much, much, much closer. Or use a much, much, much bigger bullseye. What caliber, .177 ? I don't think a .72 cal. will help any but you could try.
I don't post often, but when I do something something. It seems to me the simplest solution to the given issue is to redefine bullseye as: the impact point of wherever the pellet hits the target. Problem solved, problem staying solved. Other equally as useful life hacks also available upon request.