Typically, you can ground the 208Y120 side just as you stated. The Wye point can be directly connected to ground. Do you have any transformer protection devices installed? If not, you should consult a local engineering firm to provide you with an appropriate protection scheme.
Well, I was thinking about this one, and it occurred to me that a small problem exists. The voltage generated by the motor will be of the opposite polarity to the voltage needed to drive the motor. So, there would have to be a switching scheme in addition to the "transistor turn-on."...
It really depends on the design of the soft starter as to whether it can be used continuously or not. As to the purpose of the bypass, it can be for various reasons. The two most common are those mentioned above: to take the electronics out of the circuit (and their associated losses) once...
My suggestion would be to contact Sola. I've used the supply in question without the problems you are experiencing.
I believe the temperature range is the problem. 160 F is about 70 C and that's beyond most electronics specifications. I've seen many 50 C ambient products, but I can't think...