Morning Dan,
If fuel tap was in 'Run' position, it would suggest that there is a fault in the fuel tap, as the diaphragm should remain closed; due to their being no engine vacuum to open it.
This does not mean that there is not a particle/foreign body/wear allowing fuel to flow into the carb and then into the engine; so the float bowl needs to be dropped and the float needle, it' seat and the pivot pin all need to be inspected for wear/obstructions. Having got this far into the guts of the carbs, I would renew the float needle, it' seat, as a matter of course, even if the wear appears minimal. You don't want your wedding tackle to be flambe'!
You will also note that the carburettor mountings onto the cylinder head and rubber moulded hoses leading back to the airbox can make the removal and replacement of the carbs a vexing operation!
Check for splits in the mounts to the cylinder head. If all appears sound I would recommend soaking all four inlet tract rubber mouldings in 'ArmorAll' in a plastic tub (no need to immerse, just give them a good coating), then a good massage. This will remove a load of dirt, if present and make the mouldings more pliable. Give the mouldings a wipe down and then use just a wee touch of 'ArmorAll' to act as a lubricant when reassembling.
I have persevered with the vacuum taps on both Sally (twin shock 600) and The Mono (SRX400 monoshock with XT600E engine). I just use 'Prime' for initial startup and then switch over to 'Run' when running. Because the threads were stripped in Sally's fuel tap body, I used epoxy resin to hold 2 pieces of threaded rod as studs into the tap body and then used self-locking nuts on the outside to hold the tap to the frame bracket. Whilst other taps may fit, the whole design/position of the tap makes it difficult to attach an alternative, neatly, so far as I am concerned.
Steady away and good health, Bill