I don't have any ideas to add, but I hope some of them works. If not, I'd go with happylabs suggestion "If all else fails, ditch the boyfriend and keep the cat.

Does Jax keep getting up there because he wants to look out the window? That's Fister's reason for sitting on the kitchen counter here. Does your boyfriend not want him there because he needs the space for work, or is it because of dirty paws? If so, perhaps it would be easier to just have a damp cloth laying there at all times and just wipe the counter before use.