The SGL would be much, much harder than the JWST would be, and the JWST was already stretching our capabilities.
The SGL needs to be 650AU away from us. Voyager 1 and 2 are currently 165AU and 120AU away.
The JWST is 0.01 AU from us.
And you can only look in one direction after the probe finally gets into position. Once you're 650AU away, it's not really feasible to move "sideways" far enough to look at something else.