Great that it lives on!
I would have thoughts the balance belt deletion would cause the rougher running but would give a few extra horses?
The balance belt doesn't affect the running of the engine, but it is there for creating vibrations in the opposite direction from the vibrations created by the engine's normal running, so there is less total forces transmitted through the engine mounts into the car.. Without the balance belt you can potentially feel more of the vibration in the cabin, and a balance belt will somewhat mask an engine that isn't running in tip-top condition, for example you might not feel it if a cylinder isn't firing as well as all the rest if the balance belt is on, but you'll definitely feel it with the belt off. In my 156 2.0 TS when I removed the balance belt, I also removed the 1.4kg bottom pulley and replaced it with a 300g billet alloy one. Any slight roughness in that engine was transmitted through to the cabin, but when it was running perfectly there was no more vibration than before, even driving up an incline in 2nd gear at very low revs it would pull cleanly, with no vibration. The balance belt absorbs approx 7hp when the engine is running at 6,500rpm, I certainly noticed my 156 was a lot nippier in 1st & 2nd gear without it on, but then I did lose 1.1kg of rotating mass from the engine by swapping the aux driving pulley too. The balance shafts turn at twice the rpm that the crank does, so they'll be spinning at 14,000rpm when the engine is at max revs!
One of the best things about not having a balance belt fitted is that they can't commit hari-kari and take the cambelt out with them like in this case. It'd be better if the balance belt was external of the cambelt covers, but unfortunately it isn't.
The owner here is in a difficult position - if he'd driven a couple of hundred more miles in the car, it would have properly failed, bent all the valves and needed a proper head-off rebuild, at the very least. As it is, given how far out the exhaust cam was I would say some of the noise we were hearing was probably very slight contact in the engine, but with the timing back to factory positions it is giving good even compression so we can at least say there aren't any bent valves. But whether this incident has caused any damage, which might surface in the future, we don't really know without pulling it apart.