Well, that flat spot would be tied to the needle (height typically) more than anything else. It'd be worth popping off the diaphragm covers and pulling the needles to see what's going on there. If there are shims lifting the needle, then remove them and see how it goes. If there aren't any, put some (2.5mm washers are what I use ~ 2 or 3 of them tend to do the trick) under and again, see if that makes a difference.
They're quick and easy to get to, so you should be able to run a few tests in a typical day and see what's better and what's worse... then just keep going in the 'better' direction till it starts to get worse again, and then go back a step or two.
Best of luck.