For the supersets, as little as possible between exercises and shoot for definitely under a minute between sets. Remember than whenever you’re doing the second exercise, you’re still technically resting from the first, so it’s not as short as it might sound.
For the straight sets (the mechanical advantage work that’s not superset with anything), I’d try to stick around two minutes or so, give or take depending on your overall conditioning. They’re “only” sets of 4-6, so it’s not super-heavy that requires a ton of recovery and it’s not super-high rep that creates a ton of fatigue or oxygen debt.
Feeling stiff-arm pulldowns in the tris isn’t uncommon because they’re contracting statically through the rep. Try playing around with your elbow position, either a little more bent or a little more stiff, to get more emphasis on the lats. You could also try a rope handle with the hands touching, instead of a palms-down grip on a straight bar.