One thing that hasn't been mentioned yet that seems very noteworthy to me is that the 4s can also be snaked via the bottom left, making 4s the most flexible chain in the entire setup. You can snake them with 3 4s through the top left or 4 4s through the bottom left while you need 5 6s and 4 5s to snake them in the only realistically possible way.
I'm not even sure that mine is the more aggressive approach. Your approach commits you into 4s over 5s, making your only way to victory getting exactly 3 4s and less than 4 5s. My approach doesn't commit me to any chain, I can still snake any combination of 2 of them, I have only committed to needing 4 4s instead of 3 for snaking them. If I have a shortage of 6s I can go bottom left, if I have a shortage of 5s I can still go top left.
I also don't really like the suggestion of going 4 in the center. I see the benefit of keeping your options open as much as possible but it'd leave us in a spot where we have a lot of catchup to do to get even on the 6 chain in comparison to the 6 in the middle approach.
Unfortunately I don't know which approach is best but I like mine the most. Yours hard commits to 4s over 5s while 4 in the middle/6 to the east leaves the 6s in an awkward spot.
Also note that the problem you presented is actually rack 5, not rack 6