I will let Hugh answer but I would also be more than happy to use a mechanical relay.
Ac relays are horrible and are not very happy at 50/60 Hz, at low frequencies I doubt that the shading bands would prevent them vibrating. Rectifying to dc solves the problem.
This relay is only closing on the magnetising current of the transformer if you get it in below cut in. The thing will only open at very low voltage just before the mill stops and it should break the magnetising current of the transformer with no problem, perhaps an RC network across the contacts would be desirable. The contacts don't have to withstand or break the 300V.
I see no problem with a solid state device except that I can never understand the control circuit requirements, the data sheets just don't seem to make sense and I am not sure how you decide when it fires. You need to hit it above prop stall when it is accelerating but ideally before battery cut in so that you have a rapidly rising voltage then it won't chatter ( or chop if that is the solid state equivalent).
Flux