Thanks for the good input everybody.
(at least) 2 things I was missing: Replacement picks being 3SP/negligible bulk, and critical successes.
I think Merwyn has an excellent point about the rolls being excessive when there’s no time constraints, but I could see how the rolling could build tension when the rogue is trying to break into a dockside warehouse and the paladin is trying to distract the nightwatchman.
The gaminess of pick tracking is not fun, but I’d just say to buy a hundred, and instead of measuring them in qty measure them in the extra round lost fishing a replacement from your pack.
Link for the lazy