Did you see that report from the AAPA journal last month? They did a whole test on tooth counts in sandy soils and the 3 tooth setup actually created less vibration in the cut.
I talked to @lewis.troy about this same thing at the Gulf Coast Dredging meetup last spring, actually. He was running a 4 tooth on a similar job near Pascagoula and had to stop every 200 yards to clear the mud pack off the bit. The real trick with 3 teeth in that Mobile sand (I think it's that Wilcox formation stuff) is you get more space between cuts so the stuff can fall away instead of getting smashed into a paste. It also helps if you bump the RPMs up by about 50, but keep the advance slow so the teeth don't chatter on the quartz.
Hold up. You ran a 3 tooth cutterhead in Alabama sand? Ive been doing this drag work for 12 years and always thought you needed at least 4 teeth to get through that quartz heavy stuff down there without gumming up. Were you running a different helix angle or something? That just blows my mind.