Rebuilding the carbs is probably the wrong way to resolve this problem because it probably won't... brown stuff coming out the coils is NOT GOOD. The brown stuff is most likely the plastic insulation that coats the windings. I suspect it is melted and shorting which causes more heat so the problem will only get worse. You can measure the primary and secondary impedence to see if the coils are in spec. I don't recall what type coils you have (or what bike) but the coils should be somewhere between 1.5 and 4 Ohms primary impedence depending on the model where 1.5 Ohms is found with some electonic ignitions and 4 Ohms with points/other electronic ignitions. The secondary impedence should be 13K-18K or at least in that range. Both coils should be more or less the same. Primary is measured by putting multimeter probes (in lowest Ohms scale) on the two lugs where the power and ignition wire connect to the coil. Do this with the bike OFF. The secondary impedence should be measured by touching probes to the plug wire ends OR better, where the plug wires screw into the coils. You should be in 20K Ohms scale. These are good tests that will indicate a short if the values are outside what I noted.
The gas you are finding in your pipes is from NON COMBUSTION. When you run on two cylinders (or 3), the non-firing cylinders are still drawing gas. This isn't burned and ends up in your pipes AND IN YOUR ENGINE OIL. You had best change your oil.
Fix the coils. Once they are fixed, you are in a better position to evalutate, what, if anything, needs to be done to make the bike run right.