I'm glad they're emphasizing the genre/style aspect of HP with specific modules, or at least approaches to modules. The half hp default is causing some consternation, and I'd go with something like Chris_Nightwing's approach where restful environments allow one to rest better. That allows a trade-off between going to town (or equivalent restful environment) and staying in the field. Returning to town generally has a large minimum time requirement and the PCs risk events occurring in their absence to which they can't respond, but once there hp are gained relatively quickly and reliably. Staying in the field generally has a low minimum time requirement and the PCs can be more responsive to local events, but the hp are gained more slowly and less reliably due to possibility of disruptions. On average neither of those should be the "right" choice, and if one of them obviously is in every circumstance you should probably use a different module.
My preference for how the hp themselves might be gained in this middle-of-the-road default is this: half your currently missing hp (minimum 1 or perhaps level or Con modifier), with adjustments for environment, probably by factors of 10% to keep the math dead simple. This means that after a long rest in a typical environment a character always has at least half hp, while most have more, but the actual hp gained has diminishing returns. In effect the "low" hp return quickly and the "high" hp return slowly. For example, if a character has 100 max hit points, 0 current hit points, heals 50% of missing hp per day, and has minimum healing per day of 1, then they wake up with the following hp totals: 50, 75, 87, 93, 96, 98, 99, 100. In any environment one can rest up to full with enough time. As a rule of thumb a week under normal circumstances will be enough to top off everyone.
This also has an interesting impact on the incentives for healing magic because if a character with 100 max hp and 0 current hp is healed for 10 hp, that 10 hp really doesn't impact the time it takes to get back to full. In contrast, if that same guy is at 90 current hp that same 10 hp spell might save days of healing (90->95->97->98->99->100). That makes healing magic really good at two things: saving a life from imminent danger, and topping off a party to save time. Healing magic is relatively poor compared to natural healing, however, for trying to keep a beat-up party adventuring day after day. That doesn't really diminish the cleric's ability to be a heal-bot (assuming we don't change how cure spells work) but it does mean that natural healing is often the much better use of resources, hopefully reducing heal-bot pressure. It might exacerbate the 15 minute workday, though, to have that first long rest be so valuable, assuming the PCs are in an environment that makes it that valuable.