It's kind of difficult to understand what your problem is, (and your voltage numbers aside) your first few attempts in both videos shows the ball kick up cleanly. Does this not translate into the game?

It's not likely that the ball would need to keep kicking from that VUK over and over and over again in a row during normal gameplay anyways, as it's not often in that area in the first place. The MPU will have nothing to do with how this operates beyond the switch. The switch just tells the MPU ''hey, we got a ball here, get the solenoid to do it's job'' I will need to look in the manual for that VUK, but is it run off an under playfield transistor? Those things like to get flakey.

Have you done the recommended grounding mods and cap replacement in the cabinet? What is happening in game that causes concern? Does it not kick the first to three times as shown in the video?

I would go back to the original coil if it's good.

If you're locked on, you have a bad transistor. 2n3055s on the driver board with a TIP102 equiv, pre-driver. You shouldn't have any voltage if the fuse is pulled, which may indicate some kind of hack or bypass, show some pictures of what's going on under the hood.