The results of this competition have recently been announced. Go here. Apparently all 29 essays that won a prize will shortly be freely available to read. I'd just like to make a few comments.
By far the main obstacle to an acceptance of an afterlife is the notion held by the intelligentsia that an afterlife is an "extraordinary claim". Any evidence, no matter how persuasive, is typically simply written off as not being extraordinary enough. This being so, simply outlining the evidence in its various forms will be insufficient if we hope to convince skeptics, particularly so for those of an academic persuasion. The question of why an afterlife is considered to be an extraordinary claim needs to be addressed and rebutted. This involves underlying philosophical issues (e.g. does the fact damaged brains lead to damaged minds entail the former produces the latter as many skeptics allege?). Unfortunately, since the competition explicitly asked for the best evidence, I fear none of these essays will devote much space to such issues (the explicit emphasis on evidence is the reason why I didn't submit an essay to the competition myself).
It would have been far better if the competition were open to any essays that persuasively argue that the survival (afterlife) hypothesis is a reasonable one and, furthermore, more reasonable than the annihilation hypothesis. The essays could then have had the option of either simply addressing the evidence, addressing the underlying philosophical issues, or ideally, addressing both. Then the essays, as a collective whole, would be more likely to present a more rounded and robust appraisal of the various reasons to regard the belief in an afterlife as being a reasonable one.
The problem with all the pro-afterlife material that currently exists is that the vast majority of it doesn't touch the philosophical issues and this competition simply perpetuates this imbalance. My suspicion is that most of these essays will largely regurgitate the evidence that is already out there and will do little to persuade skeptics. But we shall see.