The shudder could be rear suspension related, ie weak springs and/or wheelhop. Make sure that you are not confusing those. Make sure there is some freeplay on the pedal, and that the rear tranny mount is 100%,and that the pinion snubber is installed.
I agree with you that if it slips in 1st it should be worse in higher gears at the same rpm. I've driven loaded grain-trucks that didnt slip 'til 3rd.
BTW; a good 383 with 3.23s and a 4-speed should annihilate any size tires you can fit into a stock A-body wheelhouse; both sides. And 2 gears. So if yours is not doing that, I suspect it's not slipping the clutch; OR I'm reading your symptoms wrong.