Heyah! Good questions I should be in a good position to give some answers, working on a very similar setup in wheelz2.
Happy to be
Word of warning, I just muddled through my IK setup with trial/error/intuition - my setup is probably not optimal.
Your screenshots of “broken” IK all look cheerfully familar, I’ve had my mannequin fold up in very similar looking uncomfortable poses 
Please do post screenshots of your animation BP and I may be able to give you some better information - a video of the current state of affairs would be handy/fun too
FWIW - my setup is:
the bike has components for:
-attach point for rider (seat)
-targets for hands
-targets for feet
-target for spine
I use FABRIK to attach the neck/head to the spine target, and two-bone IK for the rest.
In the animation BP - I strongly recommend setting some “default/testing” values - so you can better know if it is your IK setup at fault, or the data you are feeding it.
FWIW - to transform the IK targets into the correct space for the skeletal mesh, I get their world transform, then subtract the skeletal meshes position, and apply the inverse of its rotation (i’m tempted to watch the video you linked to see if they have a better method)
As for physics being broken when you mount the vehicle - first off, do you really need to have your character off the bike? Everything (including the IK) is much easier if there is just one actor.
I’m tempted to switch back to this method in wheelz2, though it is nice to be able to get off the bike, it is by no means a core part of the gameplay. IK is solved, but networking still needs some work, it is nearly correct, with occasional issues, and it seems I need to do some more work to be able to record/replay demos without things exploding.
Assuming you do need to be able to get off the bike - the main issue I ran into was from not disabling collision before attaching the rider to the bike.
Ensure physics+collision is disabled for both the skel mesh and the capsule component before attaching to the bike.
Looking forwards to seeing/hearing more of your work! I’ll post some videos of my cycle soon too