That's a good solution but it requires that it's a busy site. Since the proposed requirements are that the hosting company might not offer cron, it's reasonable to assume that this will not be a busy site. So If we need a report to be sent out once an hour but the site is only getting hit twice a day, then scripts won't get executed on time. Remember that this is for a PHPBB Mod that will be released to other customers. If they expect the report to be delivered once an hour, they are going to report it as a bug when the site is only reporting twice a day (because the site is only getting hit twice a day).
So the question boils down to, "Can we simulate cron functionality without cron?" And I think that the answer is no. Therefore, I think that the solutiuon is one of these:
A. Set it as a requirement that for this feature, you must have cron
B. If you want this feature and you don't have cron, you must visit the web site periodically and load up a specific page in your browser.
Frankly, you can get a PHP hosting service that comes with cron for $5 per month. If they aren't willing to shell out five bucks, they aren't really serious about the site in my opinion.