Experts and BHG readers answer.
Painting Oak Cabinets
I'm not a painter by trade, so I think you would also want to speak to a painting contractor about this. One thought I have on this would be to sand the cabinets as smooth as possible, prime, sand down again, re-prime and then paint. I primer with a lot of solids should be used since that will work better at filling in the low spots. It might not be a bad idea to visit a paint shop where the professionals shop--the folks who work there really know their stuff and can help you pick the product and tools necessary to get the end product you desire.