When Lott screwed up by praising his mentor, Rove and Bush decided to attack based on last years rules. But the Lott rules are in effect.What exactly did Bush do to try to force the old rules? Sorry if I missed this in the link you gave, or elsewhere.
If you are correct about the Bush/Rove challenge to Lott being smothered by the new rules, then this whole affair is meaningless to the current power struggle. Lott's excursion into Reconstruction politics came afterwards. As you tell it, Lott already beat Bush in this.
Nevertheless, this whole affair has only strengthened Bush. Lott is vastly weakened. His hold on the Leadership is one thing; publicly, he's toast. The President has done the right thing to step aside and let Lott walk in his own stench.
I see that Lott stays, and that he spends the rest of his time as Majority Leader playing patsy to the media. Lott can not be stronger; he can only be weaker as Majority Leader. Bush can now exercise more power through the rest of the caucus than he had before. No matter what happens to Lott, he has far less power than he had before Strom blew out 100 candles.
A similar situation occurred back in 1910 with Speaker "Uncle Joe" Cannon. Granted, the House is different from the Senate, but the dynamic was the same. Cannon had become a huge liability for the party, but he had the death grip on the House. All Winter of 1909 it was a fight in the press over his future. Finally, in March, 1910, Democrats and Republican "insurgents" teamed up to remove the Speaker's power to personally appoint the rules committee. That wasn't enough for the radicals, who wanted him out of the Chair entirely. The Democrats were fine with this, as it kept Cannon as an issue for the elections that November.
The President refused to get involved one way or another. Similarly to today's situation, he publicly said it was none of his business. He had already tried to get rid of Cannon the previous Autumn, and the plot failed. Nevertheless, he kept pressure on the inside, and kept quiet without. When Cannon was reelected, essentially, as Speaker in March, 1910, he kept the seat without the power. The President controlled the rest of the Congressional session, taking almost no losses in his agenda.