Ehud Harari recommended an article to us from Tokyo Shinbun from the 21st August, which discussed factions and the Monday's election (in the form of a Q and A).
One paragraph touches on the key question first asked by Earl. It says:

Q. There are various factions in the DPJ. Will those factions affect the result of the fight [for the leadership]?
A: Compared with LDP factions, DPJ factions have weak group ties. Some members belong to more than two factions and the DPJ also has a lot of independent members. Building vote numbers by gaining factions’
support does not guarantee victory in the election.
Those members who keep a distance from the factions will also have a big influence on the outcome.

Q 民主党には多くのグループがあるが、その動きが勝敗を
左右することになるのか。
Ａ　民主党のグループは自民党の派閥に比べ、結束は弱い。
一人の議員が複数のグルー
プに入っていたり、どのグループにも属さない議員も多い。
グループの数合わせで勝
てる保証はない。グループと距離を置く議員の動きも勝敗に
大きな影響を与える。

The article does not distinguish between old/former/current LDP factions, but what it says is interesting nevertheless.

Best wishes,

Aurelia George Mulgan
UNSW, Canberra