Steve, having a vertigo spell for a minute at a time like you say you had seems very very serious. I used to have vertigo sensations. I kept a log of them, to try and see when, why etc. I probably had a total of 5-6 in my first 50-70 dives. Not since then. The biggest change I made was to descend slowly and equalize gently. (I used to blow the heck out while equalizing.) They always occured in the first 8-15 minutes of the dive. Depth did not seem to matter. Each time it happened, it happened just once on that dive. No other problems like headache, fatigue etc. Rest of the dive went normally each time. Visual orientation was not the issue; the two times I can remember clearly I had really good visual reference. Twice I remember it happened when I went rather quickly from a horizontal position to a vertical position. In my case, they only lasted 15-20 seconds - guaranteed nowhere near the 60 seconds you say. I don't think I closed my eyes though - wanted to try and stay in control, plus concentrate on a spot to get my bearings,and also consciously try to regain control of my mind and stay still since my mind told me I was spinning like a top, which I knew i was not doing. Could the quality of air in the cylinder be a factor? I don't have a problem with heights etc - do you? Like you, I too have never had problems equalizing. No change in gear, 3 mm wetsuit, fits well, not tight, no hood. No health problems, no blood pressure problems. But I do have tinnitus in my left ear.
One other unusual problem I used to have was seasickness - but never before diving in, regardless of the conditions. But every so often, (but not always) after climbing back into the boat, if it was choppy, I'd get sick. I doubt there is any connection, since they did not occur on the same dives, but that seems to have gone away too, probably just coincidence. Do you notice this yourself by any chance? Seasick pills never helped, by the way. And the pills did not affect the dizzyness, dizzyness happened on occasions with pills and without.
Take care, Steve, repeated 60 second vertigo episodes sounds serious. In my case, it seems like a more gentle approach to descending, equalizing and moving helped.