I've had the same problem with my Ruger Single Six (and even worse with my S&W 617). With the Ruger Single Six, I only see this level of lead build-up with un-plated bullets - the S&W leads up like this with anything I shoot through it.
Oddly enough, my Mark II and Mark III don't have anything like this amount of leading, which makes me suspect it has everything to do with the cylinder gap.
As far as this lead build-up causing a "disaster", I'm not so sure about that. After all, the last several shots made it though the barrel when it was in that state and I assume it didn't blow up. Also, the Single Six has a barrel sized for .22 Magnum, which means that it is a tad bit generous for .22 LR, giving it more room for fouling to accumulate.
My solution has been to use copper- or brass-washed .22 LR ammunition with revolvers, which has cut 'way down in the lead build-up. I save the plain lead bullets for my Mark II and Mark III.