bridging the ports is bad- thats basically a vacuum leak, the ports should be individually capped. If its that choking rich it points to carb issues- likely dirty. Bogging down is probably related to running too rich also. Mine runs clean and makes it into the 70's before running out of horsepower- its trying but just can't go a lot faster. OTOH mine has (I think) a somewhat faulty ecu, which I'm setting up to do some more diagnostics on... it runs great doing for-real riding until some threshold is reached after 15mins or so and the ignition cuts out. Sit by the roadside for another 10-15mins and it will start right up like nothing happened.
The petcock is quite easy to replace seals in. I was dreading mine a bit having had PTSD over it on my old Bandit but the xs's was straightforward. With no vacuum on the inlet then there should be no flow on main or reserve, only from prime. Might be the petcock gasket. You can certainly run by manually putting the petcock on reserve, then off when you shut down. But with the petcock properly serviced then the vacuum will work nicely- just hook a short length of tubing from the petcock's vacuum port to the nipple on the left-hand intake manifold.
Before you start buying stuff better get the carbs apart. If they've not been overhauled then you'll likely need bowl gaskets and float valves, possibly new floats also. The good news is all that stuff is easily found on ebay et al, and easily replaced. The carbs are not hard to service or get on/off the engine.