I would say that diversity isn't something that's easy to reenforce, but I do think it will occur as a natural consequence of optimizing for shorter chains of thought according to a wide variety of problems. Of course, the nature of the data may lead it to do brute force, but that can be fixed with clever fine tuning.
I am not too sure about shortening the CoT tokens explicitly because different problems will require different length of proof - some require half a page, whilst others will require 10 pages worth of tokens. As the graphs in the paper indicate, there is a huge penalty on short reasoning lengths, below a few thousand tokens.
For diversity reward, my thinking is basically looking at reasoning tokens in latent space - taking semantic similarity between subsequent chains, and if they are extremely similar, penalizing it.
