The first thing to mention is that it's common to exchange phone numbers when making or accepting a couch request. I basically require that myself, since if you're going to trust someone with your place of course you should trust them with your phone number!
It sounds like the only solution for your dilemma is planning stays further in advance. You are just not connected enough of the time to plan stays on short notice. There is the additional problem of delays from the hitchhiking, and that's also going to make it more difficult, but you'll just have to make that situation clear to your potential hosts and have backup plans.
I've seen couch requests made a few hours before arrival and I've seen it a month in advance. You probably want to get efficient in notifying people about your progress (meaning your location) whenever you do get internet access because, again, it sounds like that's your only communication method.
To answer this question:
Have I missed some obvious way to use the facilities offered by couch surfing? Is there another service that works better for vague wandering travelers to surf couches? Is there some equivalent a bit more like a chat room or such where I can tell an online travel community roughly where I'm going and get couch offers rather than writing to each person individually which is the only way I'm aware to use couch surfing?
I would say use groups. I there might be some chat things available, but I don't know of it, and that's not a good sign. Lots of people, however, use groups. It's not everyone, but it is often some of the best connected local hosts. There are also "SOS" groups, for people who wind up in a city and don't have a place to stay. The turn around won't be as fast as what you have in mind, but I know some of those SOS groups encourage people to have email reminders turned on so that they can reply quickly.
That might help a little bit, but what you're asking about is a rather tall order. I hope you stay on top of your backup plans and have a tent with you.
Updates
Since I left this reply, Couchsurfing has changed some things about its system. Now, instead of requesting people directly for their couches, you can make a general request for an area, and then people will respond who want to host.
Relevant to the question: the feature could help better match you with your specific traveling needs. But again, to be a critic, there might not be as many people who check that. You need to understand people's use patterns to get the best result, and many people like couchsurfing because they don't have to use it often to get a lot of value out of it. So the new changes are relevant, but not a game changer IMO.