If I understand what you mean by "breathing heavy" (which doesn't actually mean anything in this context) correctly, its suffering from excessive blowby.

Work arounds for contamination of the intake track (perhaps including the air filter) by excessive blowby include:-

(a) A "road draft tube" (the original and worst) which just vents the blowby to atmosphere. That'd be illegal and immoral, but it'd probably work and you might not get caught, at least until an MOT.

(b) "Catch cans", bascically a filter in the crankcase venting path which intercept the oil vapour and soot, either before the blow by goes back into the intake tract (legal) or vents to atmosphere (illegal and immoral, but not quite as immoral as above). Look them up. You can buy them, but they look easy enough to make. The gloop they catch can either be emptied by hand or a drain to the sump arranged.

(c) Routed directly to the exhaust. I've heard of this being done by dragsters but am not sure of the details. Sounds a bit more difficult DIY but I suppose you could make a spacer /thick gasket with an entry pipe at a section join.

Re leaving the filter off that'll likely finish it off, so should be avoided unless you've given up on it. The air filter is the most important filter on the engine

Some bikers leave it off. They call it a "velocity stack" which probably sounds cool if you're a butt-head biker. Don't be.