My first thought is that your charcoal has gotten damp somehow and isn't catching except under direct flame.
As C6Bill said, don't chase the temps around. The beauty of the KK is the "set it and forget it" nature of the dampers. Fill the basket, light one spot, set your dampers for the target temp and walk away.
Your experience with the 50F degree difference between dome and grate initially is true to form, and as you noted, it balances out as the cook progresses.
The basket splitter is typically only used when you want two-zone heat, like doing a slow roast on the cooler side, followed by a reverse sear on the direct heat side. Or, using the rotisserie so the meat rotates in/out of the direct heat zone. While you can use the splitter arrangement to do a long low & slow cook (butts, briskets, etc.), I prefer the full basket setup with the foil barrier, as C6Bill described.