I've only done the few golfing runs necessary to get my Boss suit, so I understand everything except why would I go in with only 60 gags. How does the replenishment work that fewer gags improves my chances of getting fog back?
Let's say you go in with 80 gags, use fog and then lure (on first set of cogs). Then you do the golfing and earn a cane and a whole fruit pie. Then you manage to solve two more puzzles before the last set of cogs for that floor. You can't earn anything else because you're already full.
Okay so last set, say you trunk and then use that fruit pie (with someone else using cake). You're down two now. Next floor, trunk and hose. Then to golfing. You solve four puzzles again. You are full again.
Say the say thing happens but the next time you solve five puzzles. You failed to earn a gag that you solved a puzzle for.
It's a vicious reward. Each time you get a reward like a weak gag, it not only takes up a spot you could have gotten a strong gag in, but also it's another gag that you either need to use or you'll be deleting it later in the gag shop, which is more of an annoyance.
If you go in with some of your strong gags missing (have all level 6 gags, but diet out some of your level 5 gags), then those level 5's are more likely to get filled and you have a better chance of getting used strong gags replaced if you happen to solve more puzzles than your use of gags.