As Inigo would say, there is too much, let me sum up, if I have this correctly:
I can bury my buckets to encourage better temp?
It sounds like I should severely limit plants per bucket?
I can encourage tuber growth with potassium and phosphate (bone meal)?
If what you are currently doing produces results you are happy with, perhaps don't change it.
Higher than normal soil temps, due to being in containers or otherwise, will supposably increase vegetative growth at the expense of tuber growth. And it is the tubers we want here, not the semi toxic foliage...anyway..
Over crowding any crop can limit yields, but like most things, it is a trade off, and one wants to find a happy medium.
In the land of N P K, (nitrogen, phosphorus and potassium) (if I remember correctly from soil science degree, the K comes from the German word for potassium, but it was a long time ago)
Anyway, bone meal is good, but any organic slow release source of NPK in ratio of around 1-2-2 up to 5-10-10 is good to promote tuber growth. Higher N ratios OK at beginning when one to get the plants of to good start..