Well, one thing that comes to mind is stressed yeast. You said you changed yeasts- what did you start with and then end up with? Also, do you use a starter? Dry or liquid?
From John Palmer's howtobrew.com book on off-flavors:
Yeasty
The cause of this flavor is pretty easy to understand. If the yeast is unhealthy and begins autolyzing it will release compounds that can only be described as yeasty. Also if the beer is green, too young, and the yeast has not had time to settle out, it will have a yeasty taste. Watch your pouring method too, keep the yeast layer on the bottom of the bottle.
You need yeast to carbonate your beer- so it's a good thing. But it shouldn't have a yeasty taste, as you know. I'd keep in secondary at least two weeks before bottling and then rack off all the trub very carefully into the bottling bucket and then let it sit in a warm place without disturbing it so the yeast can compact to the bottom. I like Nottingham yeast for several reasons- one is no starter is required and it tends to flocculate out pretty well and you can rack off of it. And in the bottle it stays pretty compact on the bottom so you can pour your beer off of it easily. I'd keep the primary temperature around 68 degrees, too, if you can. I'm thinking that a conical fermentor and/or kegging is not going to help if you can't pin down exactly what's wrong. Filtering and force carbing would get rid of the yeast flavor, but also strip the flavor out of the beer, too.
I'm not sure what else to suggest- I"m sure some one else will have some great ideas for you.