Notice also that the bound on \beta is not quite right. You are assuming \gamma = 20\% in which case you get 2\beta + 0.6 > 1 - \beta which implies \beta > 0.4/3 \simeq 13.3. However, if \gamma = 20 then there is a 20% chance that the next proposer will not have seen i late and therefore would not reorg it. This needs to be taken into account. This of course without taking into account the nodes that are not reorging (eg. everyone but Lighthouse and Prysm as of today).