The next thing *I*'d do, as you've found a pinout and datasheet for the phase control chip, is extend the motor wires so I could reassemble the casing to hold all the motor parts in place and be able to check voltages, waveforms etc. while its actually running. I'd probably strap the body down with cable ties to an improvised cradle screwed to a plank of wood, and similarly mount the control wheel so its not all flopping around when I try to test it.
Be careful, its all mains live, so is a serious shock hazard. If you haven't got experience with non-isolated mains power control circuits (e.g, working on the primary side of SMPSUs, or on VFDs or similar), this probably isn't going to be the easiest repair project to start with.
Hint: Hand-holding test probes on a live mains board is risky. You can get away with *ONE* for brief go/no-go checks if the board layout is low density and its firmly secured so it cant move, and there's somewhere safe (and fully insulated) to rest your hand or arm, otherwise (and always preferable if you need to study a waveform or concentrate on a reading, or if the board is difficult to secure firmly), you need to solder on wires to bring out the points you want to measure to connect to your probes. For a fine pitch SMD board like this I'd probably run Kynar wirewrap wire through 1mm bore sleeving, to get a fine enough wire to solder to small pads without risking ripping them off the board, with enough insulation to be reasonably safe to use. At the probe end, the female contacts from a PC IDE drive 'Molex' power connector (e.g. stripped from a dead PSU) fit most multimeter probes if you dont have an insulating cover fitted to the probe tip. Some heatshrink sleeving over the probe connector will be required to avoid exposed bare metal. Connecting to a scope is more problematic - you *SHOULD* be using an isolated differential probe, but if you are using two channels differentially, consider fitting BNC adapters to your probes and connecting the test wires to the center pins of a pair of BNC sockets, with their shells connected together.
In all cases the test sockets should either be securely mounted with the probe in them properly supported, or you should add insulation over all exposed metal, preferably both!