I did an older LM465 with out Soft Start and used a Sharp SSR. Also removed all the Local Control Sensing parts.
The module does respond to All Lights On and All Units Off.
If you dim it. It stays on until the drive to the SSR is too low to keep it on.
There is virtually no current on the output, except for the leakage of the SSR in question. With mine I could not read any current with a meter and a very low current requirement LED bulb just barely glowed. On a regular LM465 it was at half brilliance when off.
Not too sure how the new soft start ones would work and how close the instruction's would match. My guess is the soft start would just start a second after the on command as the drive to the SSR would be ramping up.
Both the Sharp [one I did] and the Crydom version are in the Lamp Module Modification Area:
http://www.idobartana.com/hakb/index.htmI can give PCB Silk Screen Numbers for the older before soft start LM465 modules and exactly what I removed.
I found the 120 volt Sharp SSR was fine. Not 15 amps for the ratings unless you do the extreme heat sink thing.
I believe the Crydom mod can be wired to a bigger external hockey puck style devices that maybe able to do closer to 15 amps.