The transformer doesn't overheat due to reactant current, but because inappropriate control leads to false triggering. It's no problem to modify the control algorithm in a way, that even unloaded transformers (e.g. with a defective lamp connected to it) can be phase angle controlled. That's state of the art in lighting control (with analog trigger circuits) since decades.
Compensation of reactive loads only works with sine waveforms, but you don't have it here, furthermore you get high current spikes with phase angle control and connected compensation capacitors. That's why I said, it's not helpful. But mainly, it's not necessary. The apparent power consumed by small transformers can be usually ignored for power quality considerations.