"Free" in the sense that Richard is using it is "free to be acted upon". His whole question is, "Why do you act as if I could believe otherwise?" That is why I have focussed on beliefs. The suggestion from him is that if determinism is true then there is no reason to think that he could have believed otherwise. This is false if determinism doesn't entail modal collapse because if hearing an argument changes the antecedent consequences in which a belief is formed then the belief formed on hearing the argument can be determined whilst not being held necessarily if the argument could have not been presented (had he not heard the argument, his beliefs would be different).
First of all, even if you have interpreted Richard correctly---and I don't think you have---you still haven't shown that LFW (in the sense of freedom
to act upon our wills) is false. The Darth Vader example only goes to show that we do not have complete freedom to act out our wills. However, we could still have
limited freedom. That's why I mentioned before that just because some of our willings are free doesn't mean that all of our willings are free. For instance, even though we cannot freely believe in Darth Vader, we might still, say, freely catch a baseball thrown in our direction.
But, I have never heard of anyone, when discussing LFW, requiring freedom of action.
Second, even if we decide that LFW is false, this does not imply that determinism is true. LFW, as I understand it, is the conjunction of two component theses: (i) free will is incompatible with determinism; and (ii) some agents really do have free will. As a consequence, LFW implies that determinism is false. However the converse does not follow from this---that is, it does not follow that
(1) if determinism is false then LFW is true.
Now, you have argued that Richard should accept (1) because he accepts LFW. But if you give him a defeater for LFW---as you aim to do---then you will undercut that line of support for (1). This means you need an independent line of support for (1), to make your argument work. But, I do not see how this is possible.