It took a bit of time, but its fixed now. In the end there were a just a few small adjustments to make, although it was a learning process to get there. The movement had to be pulled entirely out of the clock and operated on the bench for a while to figure it out.
Its a beautiful mechanism. I was actually tempted to leave it out of the clock and just operate it exposed, but I gave in to better judgement and reassembled it. Works great now.
Here's a couple videos of the mechanism in operation.
The root problem was that the hour snail, which you see in the centre and has a different size step for each hour, was off by a couple teeth. However, there were a number of slightly loosened or slipped parts which meant that after fiddling with it, it started chiming right through the half and three quarter hours together. It was advancing its chime by one hour every 45 minutes while that was happening. A slight adjustment of what i am going to call the chime wheel (I have no idea the proper name), and that was corrected.
And yes, there are a few (30+!) years of grime built up in there. A future project will be to do a total overhaul and cleaning... but I think I'll get a bit more experience on clocks before I try that.