Beautiful clock.
Reading this thread way late, good to see your perseverance won.
Something I noticed unaddressed, when you adjusted time and found the second hand advancing forward this addressed multiple issues.
First as mentioned, the crutch pushing at feather. A flexing point. Second, excess play on crutch friction fit. Both points mentionr. 3rd, no mention of crutch foot gap maybe excessive.
These conditions definitely contributed to the escape (ew teeth advancing through palettes) running and advancing second hand and NOT holding firm resistance, so that clutch could slip.
The combined factors and perhaps a shallow anchor depth and excessively strong clutch grip bullied the escapement to advance.
What I would have done at that point was reach in with hand and held escape wheel from turning (perhaps blocked rotation with metal rod) and then advanced minute hand gently to see if clutch would give.
In other words all of the clutch issues may have been avoided, it may have been adequate as was.
Not being critical. Just pointing out something I noticed. On a recent clock I have acquired. It's clutch arrangement was a little more uncommon. The minute hand has cannon that rotates on center shaft like yours, but the clutch is much like a watch clutch as a dimple made on the minute hand tube (a crushed portion of tube) provides the grip/slip.
I forget exactly now and too lazy to get up off couch and look, but I think the center shaft on mine provides the power/rotation from gear train. The clutch grip/slip action is a dent on side of the minute hand tube (minute cannon). (I got off couch, yep I was right).
So the minute cannon tube slides onto a rotating arbor. The dent on side of tube provides the grip. That is the clutch. If the dent doesn't grip enough dent it more. If it grips too much put a taper punch inside and push dent out.
So the point of that mess is that you may of had that kind of clutch. But I assume now you have established that it is cupped washer+pin. But I read minute hand sags at quarter hour (true?).
The clutch allows hand advancing independently from time train advancement(slip) yet the clutch grips enough to push motion works (3 gear train of hands) forward.
A clutch too loose hands flop and droop from gravity or lose time. A clutch too tight can result in a bent minute hand from trying to force it. (I'm reminded of the monkey elephant joke -lol, my uncle was a trip).
Pushing hands forward will speed up escape when pendulum is active but should never force escape action when pendulum is still. This means there is too much play in crutch/escape.
The crutch foot has a very minimal gap at the suspension rod. So highly suspect contributor is the excessively long suspension leader. The foot should have slightly perceived gap with rod. The foot needs to be close but big enough gap for "drop" of escape (lock, impulse, drop). Too much gap loses impulse performance. Plus foot needs to slide on suspension rod. Friction here can actually stop clock if there where no gap.
Anyway, you're doing great job..!
Btw,
The rule on clutch tightness is pushing hand backwards doesn't stop escape advancement. But that's watch world rule