I can't help you with the question about what judges will say - though they are individuals, and might conceivably not all respond the same. Nor can I give you medical advice. However, I suppose a doctor's note might make some judges watch you more carefully during that move.
If you are worried about completing the test, moving the sequence to the end, if possible, as the coach suggests, makes complete sense to me. Many figure skaters don't do anything difficult for a few seconds after doing something like a fast spin or jump that could make them dizzy. Moving it to the end might be better, though you will have to stop at the end, which is another balance move.
Is the direction your head is pointed in (e.g., up or down) the problem , or is it something akin to motion sickness, or something else?
I had problems with motion sickness when I had to operate equipment in an aircraft during stormy weather. Although in the end I dealt with that problem by changing jobs, some of what follows was a little helpful, for me:
Even if the move has a required head position and/or motion, you can still vary the direction in which you are looking with
your eyes. E.g., if your eyes look at a fixed point near the horizon, does that help at all? Eyes affect balance
a lot, so even if you have an issue with your inner ear balance mechanism, it isn't impossible using your eyes to improve balance might help a little.
Drugs can help with motion sickness and nausea, and perhaps with whatever your problem is - consult a doctor. Of course, some doctors would just tell you not to skate.
Motion sickness sometimes varies with the pace and rhythm of motion - is the test of such nature that those can be varied, and does that help?
Motion sickness and nausea are greatly affected by what you eat and drink, how much, and when. For the motion sickness problem, I was told to eat something like Saltine crackers that were high in salt, and not much of that, about a half hour before the flight, to "settle my stomach".
Even playing with the depth and speed of breathing, and concentrating on Yoga-like meditation exercises ("Om.....") might help a tiny bit. (E.g., if I hold my breath during a spin, I become very dizzy.)
(I was also told to close my eyes and lie down as much as I could - probably not applicable to figure skating - closing your eyes makes any balance move an order of magnitude harder, and lying down probably isn't part of the move. That advice also didn't work in my situation, because the turbulence would have injured me if I wasn't strapped in, and I was operating a computer.)
If any of those suggestions help, some combination of them might help more.
Anyway, I wish you luck.