Misfire/bogging down

Recently brought this bike and it's brilliant I love it! However when I'm cruising down the road and I open her up a bit in any gear she bogs down and what I think runs on one cylinder also out of one cylinder there is black oily sludge coming out the exhaust.

I did think it was a fuelling issue but I've checked and replaced fuel lines and stripped the taps

It happens if I open the throttle any more than a 3rd.

I was think piston rings/ oil seal gone and losing compression?!

Thanks in advance!

I'd try some maintenance before assuming too much.

Valve adjust
Break down the carbs, soak in carb dip, replace all the O-rings
Vacuum sync carbs
New or clean air filter
Check carb boots and replace as needed

Of course, if your bike is modified all bets are off regarding the jetting.