Yes, I know what you mean. The part you pour SN has a stronger density than the rest, probably in the same shape of the puddle formed initially. If you let it sit for long it will have different density than the rest. Pouring SN and quickly brushing might help. I don't seem to have that problem anymore.
Have you tried mixing your SN with %10 citric acid before coating (not mixed in bottle) 1+1 or 2+1, you would have more solution to coat but it seems to be working fine for me. Acid additive prevents premature fogging of paper in humid conditions, it might lessen the stain you get too.
As I said I don't seem to get that stains anymore unless I am slow to start brushing or pushing the solution. I always mix SN with some acid.