Can the Machina Paradox be solved by expanding the choice set?
No, I would not say that this resolves the Machina paradox, because it is exactly the same as the Machina paradox: the paradox does indeed require from you to look at the three possible outcomes. The M-C/W/G book discuss only the $B$ and $C$ outcomes because it is there where the paradox focuses on whether a violation of the axiom of independence may happen.  

But most importantly, Machina did not argue that all people will have preference ordering $A&gt;C&gt;B$. He argued that it is reasonable, for evident psychological reasons, to expect that some people may... So some others will have the ordering $A&gt;B&gt;C$, which does conform to expected utility framework.

The first will say "I cannot watch a movie about Paris after losing the trip - I will smash the TV!" The second will say "Well, tough luck. At least I will see it on screen and keep dreaming about it". Both seem like behaviors that could be anticipated by "usual" human beings. 

The point of the paradox is not to show that Expected Utility (EU) is invalid for all people -only that it may be violated in reasonable situations, i.e. situations that may characterize a lot of people and may happen often.  

What paradoxes like this examine and contemplate, is the degree to which EU represents adequately the "majority" of people in some sense, and so whether it is valid/useful/not-misleading as a core theoretical assumption in economic models, or not.
And this is a matter of degree, a quantitative matter. This is true for almost all assumptions in theoretical models in social sciences.