The data points to valve timing being out. I helped to diagnose and changed cambelt and tensioner on on 32V S8 with same symptoms as yours. The belt had jumped about 1 or 2 teeth on one side and 3 or 4 on the other side, there was no damage to the belt and it was not loose. The problem was that belt tensioner was not changed at last belt change(15k ago) and damper was not not working properly allowing it to bounce kind of like when shock absorbers are gone on car suspension. Or like boot lid shocks when they have failed without resistance. Shock absorber had some resistance but not even throughout the travel and almost without resinatnce in the half of the range. This allowed tensioner to move under force of spring only.While the belt tension seemed OK when static I assume it was bouncing around when running making belt slack either one side or the other. Belt was also changed as precautionary measure just in case it had hidden damage from jumping over. After belt and tensioner change and alignment with proper tools it was running well again.
On 40V engines you have chain tensioners as well that could affect valve timing, I am not talking about the worn shoes but the hydraulic part of tensioner if one of them is not getting oil pressure or is stuck in one position it could also cause the issue.
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I think you would notice one tooth out, let alone 3 or 4
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I think it would be hard to notice it just buy eye. My friend had timing out on 12V V6 which similar locking system with locking bar as 40V V8 and you could not tell it by just by looking at it, even putting ruler across camshaft pulleys it looked like it's fine and holes align up. Only by putting locking bar in place it was determined that timing was out.