We had the same problem. The eco paint store near us basically said the low/no VOC paints will never look as good as oil-based paints for trim because oil-based takes longer to dry---that's what "settles" the enamel look so that it's smooth and shiny. We had three recommended to us (by three different stores): American Pride high-gloss, Mythic high-gloss interior, and Yolo cabinet and trim. We tried the American Pride on a built-in (terrible) and the Yolo on some other trim (passable but still discernible difference from oil-based---would probably be fine if the entire room were painted with it). We aren't happy with either overall, though, and will be tackling round 2 of this when the rains stop. Since then, I've also heard that Benjamin Moore has come out with a low-VOC line that includes a high-gloss option, but haven't seen it yet. There's also a post somewhere on this board about a low-VOC option from Ace Hardware, but I didn't see it before we started our project. We also had one store tell us that with oil-based paint, the environmental problems have more to do with disposal than with off-gassing, so she suggested checking places like ReStore (Habitat's store) for old cans of oil-based trim paint that would otherwise become haz waste. I'm not sure if that's entirely true or not, but it was a compelling option given that we're trying to match existing trim. Good luck---if you find a good option, I'd definitely love to hear about it before we try again!

Are your doors flat, or raised panel? If they are flat, you can roll with a foam roller to get a more even finish. Raised panel requires more work and brushing. If you can remove the doors and lay them flat, you can get a better finish. If you overbrush the paint, it will show brush marks. Also, use a soft bristle brush. I prefer High Gloss myself. I would not use Pro Classic. I would use a better grade of high gloss finish. I would not use a poly over the paint because it will affect the color sometimes. I did my old cabinets in Polyurethane Oil Gloss White. It looked great, but because of the oil, it began to yellow over time.

I am not an expert, but that doesn't stop me from having an opinion. (grin) I use an oil based primer when I am working on old exterior wood. And I use a slow dry oil based primer. But for something that will never be exposed to the elements and isn't old wood, I'm not so sure oil primer is going to make this paint project significantly better. I use Cabinet Coat for trim work. It is satin finish, though, not high gloss. You don't need to prime prime bare wood before applying Cabinet Coat - or maybe it is more correct to say that the first coat of CC is the primer. Here is a link that might be useful: Cabinet Coat

I assume you mean the cabinets are painted with a high gloss paint. If that is the case I would purchase a product called Dirtex. It's available as a powder and is very inexpensive. Follow the directions on the box. I use it for walls, but it can be used on wood. I prefer it over TSP as it does not need to be rinsed off. A single step is always better in my opinion.