I'd prefer to know how to reduce the EMI so it would be legal -everywhere-...

The schematic that you have posted is using a MOC3021 [ optoisolator triac driver ]. This opto triac driver is random firing type driver.

In order to reduce EMI you should use a Zero Cross Detector type opto triac driver such as MOC3041,MOC3042,MOC3043 [ Suitable for 110V AC ] or MOC3081,MOC3082,MOC3083 [ Suitable for 230V AC ].

The advantage of using a Zero Cross type opto is that it will turn the triac connected ON or OFF only when the AC cycle is going thro' zero. Due to switching at ZERO the amount of EMI produced is minimum.

Using a Snubber i.e. RC and/or MOV will also help to keep surges and EMI away.

Regards,
Prahlad Purohit