That is what I was thinking also. I don't have any problems painting letters in signs I make after just routing them out and only surface sanding the face of the sign. Never inside the letters. Sharp bits will greatly improve things, even just making sure the bits are clean will help. A bit that has caked on pitch from prior use won't cut cleanly no matter how sharp it is. Also, I don't know if you are using treated lumber for this since it is an outdoor sign, but if the wood is treated lumber then there is not much you can do to about smooth cuts anyway until the wood dries out. If you are cutting it just after purchase while it is still wet then it tends to leave a lot of frayed edges and roughness instead of coming out smoothly. This will also increase the level of pitch buildup on a bit as well. One last thing, if it is wet treated wood, then the paint won't last long on it anyway. Gotta let treated wood dry out or it's just gonna be a disaster all the way around, in cutting and finishing, both.