Preferred carburetor for mild 360?

Rods aren't going to do anything at idle. It's got 15" of vacuum which will hold the rod pistons down.

The mixture screws on the front are what need to be adjusted at idle. Have you turned them at all since this began or just been running them at the baseline 1.5 out setting. Turn them out 1/2 turn to see if it helps. Those carbs are notoriously lean OOTB on cruise/WOT, but, you didn't buy it new so who knows.