Although I never had the caloric reflex test, I think I can confidently echo the apparent consensus that the balance nerve on your 'AN side' is non-functional and your brain has compensated for the deficit and adjusted, accordingly. I had a similar experience. I was in ICU for 4 days and when I got up to walk (Day 3) I was shaky on my feet but soon regained my equilibrium. Enough so that the stern and skeptical PT nurse (I think her name tag said 'Nurse Ratched') made me walk up and down stairs and navigate various obstacles in order to convince her that my balance was acceptable enough to warrant my discharge, even though my doctor had ordered my release. It was. Once home, I had a PT nurse from the VNA for 3 visits before she stated that I didn't really need her and to just do the printed exercises and walk a lot, which I eagerly did. Thankfully, I didn't have post-op headaches, never really experienced the 'wonky head' syndrome or had any problem in large, noisy environments. However, my balance is probably about 20% less effective than it was prior to my AN. I can live with that as it doesn't really affect my lifestyle in any noticeable way.
While no one can accurately predict the precise outcome of your surgery (should you go that route) the fact that your brain has already compensated for the loss of input from the affected ear, due to nerve damage, should be a benefit for your recovery, as regaining the ability to balance and navigate most places won't be a major issue.