I simply disagree. If it's set up right and tuned right and doesn't have anything wrong with that set up, it may start a bit hard when cold, if there are no choke butterflies in the carbs (pumping the acclerator is a pre-requisite, there), but should fire right up when warm.
Like within a turn of the crank (or four cylinder fires).
Todd, re-reading your post, is sounds like one of two things is happening:
1: one or more of your carbs has an inlet (Pilot) valve with some crud in it, holding it partially open and letting fuel dribble into the bowl from system pressure when the engine is shut off. That overflows the bowl a little and raw gas dribbles down into the intake manifold making a very rich condition in that runner.
It's less noticeable when cold, because the cold manifold runners need to be slightly richened when cold to overcome condensation on the inside of the runners (which is what a choke does), so that's why it starts easier when cold.
When hot, it becomes over-rich and "loads up" (an old 2-stroke term) just like it has a choke on. To clear it when warm, simply mash the accelerator to the floor and hold it there until it clears out and starts up. THEN do a carb rebuild by at least replacing the pilot valve(s) and re-setting the float levels.
Or, 2: you have an intake manifold gasket leak (I doubt it, but it's possible). Get a can of aerosol carburetor cleaner and spray it all around the carb-base-to-manifold gasket while the engine is running and watch to see if the rpms speed up while spraying. Do the same at the manifold-to-head gasket and look for a speed up there. If it does, the gasket has an intake leak and must be replaced. If it doesn't you're OK and don't do anything, but look back at #1 above.
If these two fail to produce better results, see the articles Greg mentioned above, but a carb rebuild might be in order....
gn