Another possibility is that he is simply going senile.
Given the 'plan' he went with in the books was to set up his own death, bequeath a book of fairy tales (and note the prior fairy tale comments from him, pre-ring damage), and hope Harry survives to get killed and come back in a fantastically, radically unusual way and then somehow beat Riddle after that...
Lots and lots of options.
I've written a little fanfiction, too, and the inconsistent characters/ones I personally just don't understand are a problem, like impossible timelines and world-breaking retcons.
If you choose to keep Albus and Taylor apart, or have their future interactions off-screen, that's a perfectly valid and appropriate way of handling it.
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The conversation itself was well done. Albus did little but deflect questions and go back to 'trust me, bro.' Taylor, backed by Harry, kept going back to 'here's what I saw and the logical consequences that can come of it.' Albus finally went 'youthful indiscretions!' - very like he did in the forest when asking Taylor not to retaliate lethally when attacked first with lethal weapons.
Albus hasn't seen 'children' do wars. Taylor has, and she brought up notmjust examples, but ones she can show in a Pensive.
They left with no change to either side... as expected and appropriate.
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But! Albus HAD to try to get Harry back under control, because his alleged 'plans' or possible 'hopes and dreams' or possible 'prophecies and fairy tales' depend on Harry.
Taylor WANTED to get Albus to change, because he could make war on Riddle and/or be active politically in a way that benefits her and/or give her a ton of actionable information/blackmail/combat training he's gathered over a very long lifetime.
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We also found out some critical information during that conversation:
Dumbledore twitched.
"…Alastor and several others are not answering their fires, it's possible he did not wait for me to begin organizing."
We can infer that Albus tried to firecall Moody and, apparently, at least 4 of Moody's go-to crew (4 MIGHT be the lower bound of 'several', 5 is more likely), none of whom answered.
We also hear Albus use the word 'organizing'. I'm going to lay out 13:3 odds in favor of 'raiding' being what Moody did, and that at least part of the reason all this took so long is that the sequence of events looks like this:
Hedwig arrives Moody's.
Moody security checks Hedwig and reads.
Moody hits the 'OVERTIME NOW NOW NOW' alert for his go-to crew.
Moody plans out the raids, quick and efficient.
Moody sends the info on to Aurors he trusts to ignore Albus and arrest a Marked young person in a low-threat environment, and to the Auror hierarchy in general.
Moody and his team start raiding Death Eater locations even while the message is in transit.
I'll also bet Albus said 'organizing' because that's exactly what he meant; all talking and planning and no action rapid enough.
IF this is roughly what happened, and Moody personally also believes Albus would not have moved this fast, then Taylor's credibility as a strategic asset in Moody's eyes just went way, way up. She successfully got actionable information and delivered it so rapidly and secretly that it could be acted upon before the enemy could render the information useless.
Possible consequences include that Moody goes to meet with the Potters and fill them in on what he discovered on the raids, as well as internal Auror politics/warnings.
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Separately in the chapter, the alert to trusted Defense Association members and meeting with them revealed a lot; the members paid attention to the meeting, but only a couple had wands in hand (note Taylor had pepper spray and knife in hand); those are the most wary (good) and/or spoiling-to-fight (bad) members, but the vast majority wasn't ready for immediate combat.
That's ok! All ills can be solved with simple training. We'll start with the basics; a test. The entirety of the Defense Association against the Potters (just Mrs. Potter? Too much?) in urban combat (simulated by the Room of Requirement). And then since Taylor established her credentials, the training can begin.
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Taylor and Hermione was handled well. I'll note those two operate on different timescales; to Taylor, a few days was an entire operation's worth of time, an eternity. To Ron and Hermione, it was a set of classes or two, trivial. Taylor also operates as a front-line combatant; she needs people she can depend on every minute of every day in case combat occurs or missions need to happen. Ron and school-mode-Hermione do not, nor have they had to except during combat/missions, which were very very rare (annualish).
Taylor's good at working with allies, even allies of convenience; I think she's getting a feel for Hermione's foibles... and Hermione will, in a bit, start understanding Taylor's foibles.
Taylor's foibles are more suited to surviving what's coming. Hermione's are more suited to civilian life... which, regrettably, Taylor is right about only having a chance of after either leaving to another continent or surviving - and winning - what's coming.
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Taylor's advice to consider exiting the continent as an option was very wise.