You might be able to use a really good primer, like Kilz without first removing the Varathane (as long as it's in good shape and not chipping). Then you can paint. I would use a really good oil based paint. More durable over time than Latex in my opinion.
The remodelers would likely know for sure. Have you been to that forum?

Post over at the paint forum for opinions from the pros.

I think they're going to tell you to lightly sand, prime with a quality primer, then paint with whatever you want.
Oil is no longer rated as better than latex since latex has come a long way in the last few years.
They'll also tell you to check out CabinetCoat brand paint. Check the thread below for previous posts.

Here is a link that might be useful: painting cabinets

You'll get lots of good advice over in Paint. I am a huge Cabinet Coat fan. I painted my cabs, they were dark stained oak with varnish on them. I applied a water-based primer (Zinsser Bullseye 123), then CC, which is a water-based enamel. If I had to do it over again, I'd prime with a good oil-based primer (you'll find out why if you read some of those painting cabinets posts annz linked to). Then topcoat with latex paint or water-based enamel. No need to use oil-based top coats anymore, besides, they amber/yellow over time.

Moonshadow: This information is good to know. The oil base top coats do amber and yellow over time. It is important to me though, now, to get a good match with what I already have; the oil base is doing that for me. Your information is good for me to file away for future. (Although this is not my question, thanks for the info, I know I can use all the help I can get).

I am in the process of painting mine too. Doing as suggested also. I still see the woodgrain through the paint, I like the end result.