Asking an academic for a cursory look at a paper
First of all:


  no risk whatsoever of scooping the paper


It's never possible to achieve "no risk whatsoever" when dealing with human beings.  The best way to trust a person is to know them for a long time, but even that is no guarantee.

However, I don't think scooping is a serious concern in this scenario.  Alice has already submitted the paper, which is about the best possible way to establish priority.  Moreover, if the person were to go on to publish the results, even if they claimed to have discovered them independently, Alice would be able to show that in fact she had sent her preprint to that person, so they were well aware of her work.  Similar logic applies to the possibility of posting to arXiv - I don't think fear of scooping is a good reason to avoid that.

In general, looking over a paper informally is something that one does as a favor.  I wouldn't hold out hope that a stranger would agree to do it for someone they don't know.  I think about all Alice could do is to look for people who would be well qualified (e.g. who have done related work in the field, and possibly whom she cites), send them the preprint with a polite request, and be prepared for lots of polite refusals.

But I also think this is a particularly poor time in the paper's lifecycle to make such a request.  Alice would be asking them to duplicate work that is already being done more thoroughly by the referee, for no better reason than to satisfy Alice's impatience.  It would have made more sense to ask before submitting the paper.  At this point, I think Alice should be patient and wait for the referee report on her paper.  If it gets rejected, she should make her best efforts to improve the paper, and then consider trying to have someone informally review it before resubmitting.