I have a Lennox G23 furnace with a White-Rodgers 36E24-204 NG valve that continually is tripping the limit switch, due to a condition where the pilot is putting out way too much flame. I can see areas on the plate where the limit / rollout switch sits, and the flame has deposited large amounts of soot and blackening. I tried to adjust the pilot gas flow to its lowest setting (clockwise as far as it would go), also tweaked the pressure regulator adjutment counterclockwise some to see if it would reduce the pilot flame while the unit is running... Not much success. On an intermittent pilot system, how much flame should be present on the pilot after thre main burners are lit and running? Is this just an issue where the gas valve cannot regualte correct pressure for the pilot anymore?

Sounds to me like the pilot orifice is to large or someone at one time opened it up. I gas valve is limited as to how much pilot control it has. This kind of thing happens when a natural gas furnace is converted to propane and someone forgets to change the pilot orifice.

This is a furnace that's at my wife's quilt shop... I recently had to replace the igniter module. Is there any reason to suspect the gas valve?

Soot is not normal. If the gas valve turn on and off then it is functional. Take some gas pressures before and after the valve and post results.