There is another possibility that the paper doesn't canvass (understandably, since it would be a paper in itself), namely, whether the similarities, plus the lack of evidence for Berkeley's influence, might not be indicative of a common influence. There is, in fact, a plausible candidate for such influence, at least at first glance: Nicolas Malebranche. Berkeley certainly was a reader of Malebranche, and was heavily influenced by him; in fact, although it isn't obvious to the reader who doesn't know Malebranche, perhaps as much of the Principles is devoted to addressing Malebranchean issues as is devoted to Lockean ones. Edwards is trickier, and I lack the expertise on him to say much that is definite. However, as Trapp notes, Malebranche, unlike Berkeley, was in the Yale library at the time (as was Norris, the leading British Malebranchean). And it has been argued (by Paul Copan, for instance) that the evidence for Malebranchean influence on Edwards's thought in general is reasonably strong. And I notice in particular that some of Edwards's comments sound (much as Berkeley's comments sometimes sound) the way you would expect comments of a young Lockean (in a broad sense) who was impressed by Malebranche to sound. For instance, this, qouted by Trapp, could be said by either Malebranche or Norris:
The idea may be resisted, it may move, and stop and rebound; but how a mere power, which is nothing real, can move and stop is inconceivable, and it is impossible to say a word about it without contradiction. The world is therefore an ideal one; and the law of creating, and the succession of these ideas, is constant and regular.
In fact, Malebranche was famous for insisting that (in creatures, at least) power was nothing real, and that the world was an ideal one, and that the regularities we perceive were not due to any causal powers in material objects but to general laws. Of course, Malebranche was not himself an immaterialist; but his claims about material objects are very obscure. The most natural reading of them (not, I think, quite correct, but certainly the most natural) is that he thinks that the only (good) reasons for believing that there are material objects are doctrines of faith -- the creation and the Incarnation in particular. Thus, it's very easy for a reader of Malebranche to take the small step to idealism -- indeed, we know that Berkeley certainly did. So there is at least a superficial plausibility to the idea that Berkeley and Edwards may both have derived (in a loose sense of 'derived') their idealism from Malebranche (perhaps in Edwards's case via Norris in part or in whole). This possibility, incidentally, does not exclude Trapp's own suggestion, that they were both reacting critically to Locke's representationalism (we know, in fact, that Berkeley was doing so -- he was also reacting critically to Malebranche's representationalism, if we want to call it that). And it would go some way to explaining the intriguing similarities that go beyond the mere fact of having similar philosophical projects.