'97 M900 dirt in carbs..?

Hi,
All my own fault, I suspect.
By accident, I had to run my M900 down to the dregs in the bottom of the tank. The engine was misfiring as I pulled into the filling station, and I hoped that it was merely fuel starvation. Having refilled the tank, the bike fired up ok, but the tickover was uneven. Having taken the bike out a few times now, starting is fine, but pulling away is hesitant and one cylinder is clearly misfiring. Beyond about 1/3 throttle the bike is fine; but slow running around town or (worse) around a roundabout is a bad experience.

I haven't done anything in the way of investigation or diagnostics yet, beyond browsing the relevant chapter in my Haynes manual. I suspect that some muck has been ingested into at least one of the carbs and is blocking the jets of (possibly) one of the carbs.

Before I invest in carb service kits and the like, does anyone have any words of wisdom?
Can I remove the carb jets for cleaning without having to re-balance the carbs after the event; or will rebalancing be a necessity? I accept that a rebalance may be beneficial anyway, but that is the one bit of kit that I lack.

Thoughts? Anything beyond "how dumb to run the fuel so low" would be appreciated.

Graham