Timing changed after Cap + rotor swap?!

The reluctor/pickup or points, etc determine firing of coil. The cap and rotor are along for the ride.

The mechanical advance could have been stuck in a slightly advanced position when static, now with dinking around, it's snapped all the way back to where it should have been resting. That vac adv one is an interesting deal.

Re-time the engine, check total and move on if everything is OK.

I can't believe you had to say this once, let alone twice.
THE RELUCTOR POSITION IN RELATION TO THE PICKUP COIL IS WHAT DETERMINES IGNITION TIMING.
(Same with points and the points cam)
The cap and rotor have ZERO to do with timing but only relay the spark to the respective terminals inside the cap.
The produced spark is either in range of it's terminal or it isn't.

Think about this.
You can take the cap, rotor and all the plug wires out and your coil will still fire in correct time when the engine turns over.
This can even be verified by putting a timing light on the coil wire without it connected to the distributor and when you turn the motor over you will get four flashes per one 360 degree turn of the crankshaft. (Four flashes on your balancer with the light.)
ONE will be exactly where your base timing is set.

The cap and rotor only relay the spark and have zero to do with timing.

Also the engine would not have started at all if the plug wires were moved one place all the way around.