The triac will trigger part way through the sine wave so effectively the first part of the rise is cut off. The output inductor controls the rise time of this potentially sharp switch-on. This assumes the triggering circuit, and the diac in-line with the triac gate are functioning correctly. So I wouldn't rule out the control side just yet, particularly with so many channels looking bad. If a one-off channel was bad then I'd immediately suspect the diac, triac or inductor. Multiple channels looking bad in similar ways points more likely to a common problem rather than faults of the same type in the discrete components of multiple independent output stages.
Probing this is dangerous because of the mains voltages, but where competence and safety allows I would take a look at the inputs to the diacs on each channel and compare good and bad channels. Then I would work backwards to the opto-isolator and then onto the low voltage side of the control circuit.
Unless you think there are several different faults you don't need to debug on all 36 channels, just take a Rackmaster which has a good and a bad channel and compare step by step back from the diac.
If you can upload the relevant page(s) of the schematic here that would be useful to give more specific guidance.
Let us know.
Regards, Kevin