I've done this to an Omas Cinema LE and Omas Dama -- not because there were any problem with the nibs or angles -- but because I was merely curious about how easy it would be to remove and re-seat the nibs. I was surprised to find that the nibs on those pens were screw-in types, not friction-fitted. No challenge in that... So I reached for the Omas Ogiva Autunno, which has a friction-fit nib. To unseat the nib, I moistened a paper towel, gripped the nib, and wiggled it firmly but gently at first just to loosen it. Do not grip the nib/feed at its sides; grip it at the front and back. Sometimes soaking the nib in warm water (not hot water, but warm water) will help loosen it. You will still, however, have to wiggle it free to remove it.
While gripping and gently wiggling the nib and holding the barrel firmly, I was able to get the nib out eventually without damaging it. I made sure not to twist the nib/feed, so as not to misalign it or damage the feed in the process. Once I unseated the nib, resetting it back was not a problem. It requires a delicate, but firm touch and is not as daunting as it seems.
You may to practice removing and re-seating friction-fit nibs on less coveted pens -- at least on a first pass -- just to get the hang of it. It may be trial and error at the get-go, but once you master the task, you can then proceed with the Omas 360 and play with different angles to find one that suits you. Pointing out the obvious, you do run the risk of misaligning the nibs altogether and/or damaging the feed -- rendering the sweet spot to be nonexistent no matter the angle. However if the pen has to travel to Mottishaw's pen grotto anyway, you might as well give it a go yourself first... Are there no local nibmeisters in your area who can take on the task?
If not, then alternatively, I'm a firm believer of the original solution to every problem: duct tape. Have you tried duct taping your thumb to your palm or even your index finger, so as to retrain your hand to write without a thumb? If this won't do, then you may be able to effectively communicate the "urgency" of the matter to Mottishaw by cutting off your thumb altogether and shipping it to him -- properly iced, of course -- along with the Omas 360 and instructions to align the nib in accordance with the enclosed thumb.
By the way, my advice to duct-tape or cut off your thumb applies only
after you've first attempted to remove and re-seat the nib yourself. Methinks the procedure to remove/re-seat nibs is hairy enough that you'll require both thumbs to do so. Good luck, and let us know how it turns out.