Interesting questions. Off the top of my head, here are some thoughts.
First, when you say poop beast, you're talking about willow, poplar, cottonwood, maybe bamboo. All are fast growing, therefore not very hard wood. However, if it's a productive system you can just burn more of it
As to the question about taking up nutrients faster or slower, I would say that coppicing causes the tree to "pulse" more than letting it grow (i.e. in the year you coppice it, it sloughs off roots and doesn't take up as much material from the poop pile, but in the following years as it grows up, it will take up more nutrient than a single-pole tree) Thus, you might set up a poop beast coppice system with 7 tree stools surrounding your poop area, and each year you coppice one of them. That way you always have a few trees in full growth mode while others are recovering from being coppiced.