Assuming a single-string pickup behaves pretty much like a "normal" six-string pickup (which I don't know to be the case) I'd say that your buffers can be similar to the sort of thing we'd use on a typical pedal (so >500K input impedance would be nice, and BJT, FET, or op-amp as you see fit).
The mixer part is a simple stereo op-amp mixer. You'll fins loads of schematics for such a thing. Ones with panpots for the inputs are less common, but they're out there too. For example:
http://www.all-electric.com/schematic/simp_mix.gifThe one in the bottom right is the one you want. It shows various types of input you could implement, but for your application, you'd need six of the "mono input with pan". You can also leave out the second "re-inverting" op-amps (the ones with 10K/10K/47pF round them) since you don't care which way up your output signal is. So it's a simple job with one dual op-amp, plus a lot of pots!
If you want insert points for each string, I'd put those between the buffer and the mixer. Since the stuff you insert should have a low output impedance, the mixer's >10K input impedance won't be an issue.
Splitting the signal after the buffer really isn't a problem, despite your worries. The load that the buffer sees will be the parallel combination of the three destinations (assuming you have all three plugged in, which you won't always). Parallel combinations of resistance or impedance always reduces the overall value, but since a typical op-amp can drive loads of a few KOhms without too much sweat, it's very unlikely to be a problem.
If the Arp is going to be fed a signal which contains all six strings, then it would be best if it had its own separate mixer circuit, which could be a super-simple affair with no individual level controls or panpots, just the six signals mixed down to a single mono output to go to the synth. That's a one op-amp job.
I definitely agree that you should draw a block diagram. It'll get it clear in your head, and if you post it here, we can tell you if you're on the right lines. I often think I've got something worked out, but then when I start sketching it out, I realise there's several things I hadn't thought of. Seeing it in front of my eyes makes it far more obvious, at least for me.
HTH,
Tom