A Criticism of Amyraldianism?

So my brother pressed an objection to Amyraldianism and thought it important.  Here’s the context:

Proposition: If a reprobate person were to believe, then they would be saved.

Basically the question is this:  How is it that the reprobate could be saved on the basis of belief even apart from election?

Traditional Calvinism cannot countenance this proposition, as the reprobate could not be saved even if they believed, as the atonement was not provided for them.   The atonement was only provided for the elect on traditional Calvinism.

My brother thinks a powerful response is that the reprobate would be, if they believed, members of the elect – so that the atonement would be for them on the condition of their belief.  He thinks that this is sufficient to account for the proposition.

Here’s my response: 

Why would the reprobate be members of the elect if they believed?  It cannot be because of their belief, for belief does not cause election, but election causes belief.  

So if they were to be members of the elect, it wouldn’t be on account of their belief, and if not on account of their belief, then not members of the elect at all.  So this response will not work - for we’re trying to account for the truth that the reprobate would be saved if they believed *despite* their not being members of the elect. 

So you can’t use their election as an explanation for why the reprobate would be saved if they believed, for their election *follows* their belief.  If one did say something like this, then they would be conditionalizing the atonement along an Amyraldian direction - If one believes, they’ll be granted election and hence salvation.  And an Amyraldian just may be fine with that. 

Objection:  If they had belief, then that belief would be the result of election, and they would be saved.  That’s enough to account for the proposition. 

Response:  Not really, for it’s still the case that they would be saved apart from election if they were capable of having true belief on their own, even though they are not capable. 

Compare:  It’s impossible for me to live in the Roman Empire apart from time travel. But if I did live in the Roman Empire, I would have existed before the Renaissance. 

So even though it’s impossible for me to live in the Roman Empire apart from time travel, it’s still the case that *if* I did live in the Roman Empire, then I would exist before the Renaissance.
Time travel = Election
Existing in the Roman Empire = Belief
Existing before the Renaissance = Salvation

Unless you want to say that election can be, though isn’t, responsive to belief:  God would elect those individuals who believe apart from election - and we could still say that Christ died only for the elect.  This still conditionalizes the atonement in an important way and seems a step towards Amyraldianism.  

So we should broaden the atonement beyond the elect to adequately explain the truth that the reprobate would be saved if they were to believe, even though it’s impossible that they do so believe.