Hi, couple of things.
Adding filters to the fuel line may result in gas trying to run uphill which it will not do. Fuel lines should be downhill all the way.
Carbs have three connections that look somewhat alike. Fuel in, Vacuum out and float bowl vent, mixing them up gives very unsatisfactory results. Your problem description confused me as to which pipes you have where.
Typically the petcock to carb vacuum line is from the left hand carb only, it is the shortest route for the pipe. If the bike is coastered or marbled right hand vacuum is capped, if not it runs to a valve under the tank.
Both bowl vents are teed together and the long part of the t placed where no significant pressure or vacuum is applied, tucked up under the tank is a good place.
Is the new petcock the standard Vulcan one with three connections, Fuel out either side and the vacuum in the middle? Test it by sucking on the vacuum port and fuel should flow? Or the Yamaha manual operated with no vacuum connection?
'99 Vulcan "Victoria"