Hi,
I looking on the element14 website, my goto place for things electronic and may have lead you astray, good ones
capable of a decent load are more like $50.
I did see some DIN rail types, had a fairly modest load though, 100mA at 48V, my guess is that they are designed
to switch contactors on and off.
There are too the 'brick' type with 4 screw terminals, have used a few of that type at work, capable of 3A at 240VAC, may
be of interest to you for your coolant pump, not DIN rail that I saw.
I repair welding equipment for a living and I've seen LOTS of inverter type machines go bad. As a VFD is an inverter of a type
they can likewise make a big mess. I would not power one through a solid state relay no matter how good. BOB to solid state relay
to 'kick anus' contactor yes---solid state relay only between VFD and BOB/ESS/PC no. I mean the AC input side to the VFD here
the VFD inputs don't concern me that much.
Rather depends on how permanent you want your solution, as they say 'there is nothing so permanent as a temporary solution'.
Craig