Thanks for the replies - it's definitely a conundrum. As Eric pointed out, there's not a clear restriction making the decision for me on this one. Available on-site materials, cost for what can't be sourced on-site, and the ease of construction (one guy doing everything manually - no heavy machinery available) are the only restrictions I'm working with on that end of things. I've gotten so used to the whole "define the problem to find your solution" methodology...multiple solutions drive me nuts!
Our current design utilizes a pretty stout roundwood timberframing with 14 to 36 inch diameter eastern hemlock and relatively short rafter spans (maximum 14ft spans between beams with most being just 8ft). The weight of the roof isn't something I'm too worried about...it's the weight of the logs and the joinery skills used to build it that are!
Tyler set my mind going with the idea of filtering the rainwater runoff, though, and something like that would almost certainly work. Our current shed/wrap structure has a thin (3" or so) green roof (experimenting with the technology) and we initially found a lot of clay and organic matter washing out last year, just after it was installed. This year, however, the water is almost running clear to the eye. We know the ducks are getting up there and doing their thing, and we have n-fixing clover, etc, up there putting more nutrient into the run-off, but it certainly isn't as bad as it was when first put in place. As the root mass builds up more, I'm sure this will improve further, and by running the water through at least a slow sand filter, if not a cattail/reed bed followed by the filter, we could definitely harness this water for utility purposes (hand washing, clothes, dishes, etc). The utility water, of course, makes up the majority of our water use, so this would be a huge plus. In that sense, we can consider that "con" to be removed for the green roof.
As for drinking water, another thought came to mind - a free-standing catchment system on the roof as well. A few roofing panels on a lightweight frame, sized appropriately to ensure apx 100 gallons of drinking water catchment per month, could be set up pretty cheaply and piped down to separate holding tanks. With decent anchoring and proper placement, it should hold up to the wind well, and with some fencing over/around it, should be able to keep the dirty duckers off it, too
Will have to noodle on this some more before I make a final decision, but with the water situation becoming moot, the green roof certainly takes the lead in the mental battle. Construction can't start until at least next year after we've done the site prep work and I've cut/limbed/peeled enough posts and beams, so plenty of time to play with ideas still.