Mark et al,
Sorry, late to the huddle here, but I wanted to hopefully contribute something as well, as I really like this live experiment we are participating in.
Regarding unnecessary time spent on beta, I agree with others who suggested delegation; delegate the really unnecessary (for you) stuff to one or two folks, like the moderating pending suggestions part, so you can concentrate on the approving pending suggestions part. Someone to do level-1 stuff, either 1-2 trustworthy volunteers if you found them, or paid, depending on how involved the assistance duties will be. I don't know how much time you spend moderating & approving topics on beta, but if quite some, maybe at the minimum, delegate the weeding out/editing/merging/searching/etc stuff, leaving you a more or less clean pending queue for you to go through and approve stuff. MF was a good step towards the setup but it still requires human QA-like intervention. Maybe get the helpers to also tidy-up and moderate the group as well, whatever it may be that will free up your time from stuff that someone else can do.
I like the concept behind your idea of the two hashtag-step process, but maybe go at it a bit differently, using already mentioned ideas as inspiration; leave #suggestion as it is now as the first step hashtag, it's easily recognizable, well-known, and already has baggage, so just let it be what it is. Then create additional official "bucket" (stage) mod hashtags, one of them to serve as the second hashtag in your idea, maybe #acknowledged, #received, or whatever; you already have two of those bucket hashtags already, #fixed and #done, and are using them as a notification/tracking tool already, so take that a little further, add strategically-named #bucket/stage hashtags and append-use them on the #suggestion thread. This should greatly extend beta's notification/tracking capabilities.
Anyway, continuing, when some suggestion merits going to your second hashtag step, which I presume means no more talk-talk as it's now in my court, lock the thread and add the bucket hashtag for it; it's still a #suggestion, but now it's officially #acknowledged and awaiting its fate. And if you were to add a few strategic #process hashtags, depending on how much info you want to provide, you can create quite good tracking capability and let users know of the status of a suggestion during its entire lifetime: it goes from #suggestion #<1ststage> to #suggestion #<next_stage> (and/or) #<whatever-process>, ..., all the way to #suggestion #done.
Finally, regarding subgroups, in this case they may be better for using them as announcement lists, but also in the occasion if it is something beta-related but you'd like to group-discuss somewhere else besides beta. I also agree that normal suggestion discussion stay on beta.