My first plan would be to check the compression. If there is a loss in power it could relate to there being low compression caused by ruptured piston rings or ruptured head gasket.
When you say it doesn't like ticking over to you mean it runs at too high RPMs during tick over or it is just very lumpy and can't keep running in tick over. When my little 4hp was running badly (high RPMs) during tick over I replaced the carb gasket and it was fine. It also increased top end power.
Is the air filter clean? If it is all clogged up then it won't be able to breathe very well resulting in loss in power.
It might also be worth checking the RPMs it is running at then referring to the owners manual to see what they should be running at.
These are the checks I would do. Pretty simple and cheap. A carb gasket is going to cost you no more than a fiver and you can probably borrow a compression tester from someone you know if you don't have one already.
If you don't know how to do a compression test, all you do is take one of the spark plugs out and screw the end into into where the spark plug was. You then crank the pull starter until the pressure on dial stops rising, then repeat on the second cylinder. Simple
Also, you say you cleaned the jets, did you clean the bowl as well?