This helped me
Don't know if this helps axis tilt but I had much trouble working my right shoulder downplane and tended to roundhouse (especially under stress).
I saw Martin Hall demonstrate how to put your driver across your shoulders (in the front) with the driver head toward the back (handle toward the target). Assume your stance and then make your back turn (with arms holding the driver in place, I cross mine in front of chest).
On the downswing, think of hitting the ball with the head of the driver just using your downplane shoulder turn.
This move will feel different (it did to me) but it gets you to move your right shoulder downplane and as it does you will feel your left hip slide a bit to the left to accomodate this move. If you don't move laterally with your hips (think left hip to the left) then you can't get your shoulder on the right plane which is key to getting on the right downswing plane.
This single drill and change, dramatically improved my ball striking and I use it to warm up on the range and in between shots on the course.
Try it, it will work. You will feel what everyone means by down and under much, much more.
I have used the left shoulder up for about 6 months and it will work but working on your right shoulder down is much more effective.
Don't get me started on twist away (to finally kill that slice forever). It works too.
Good luck.
PS: I recommend Martin Hall's book, Myths (google it). It is great for drills that will help with TGM.