I'd be very interested to know what suppliers you'd suggest.
Because you only need a few feet, I suggest you make your own by twisting together several strands of magnet wire. For example, 9 strands of 25.5 AWG magnet wire will give you 16 AWG. I think Percy Audio still has some Ohno Continuous-Cast copper magnet wire in stock. Chimera Labs used to sell the same wire cryoed for a reasonable price. That would give you the wire quality you are seeking. Otherwise, there are numerous sources for ordinary magnet wire, including Radio Shack.
Ah yes. That's a pretty good idea.

Providing all is still in stock, Percy Audio has the following gauges:
AWG20 - 2.53 strands is the equiverlent CSA
AWG21 - 3.19 strands is the equiverlent CSA
AWG26.5 - 11.41 strands is the equiverlent CSA
Unfortunately, none of them appear to be a close integer match as far as thickness is concerned. Thankfully, I have standard uninsulated wire of this kind, so could experiment until I got a practical design.
Any thoughts on which combination is best? I imagine AWG21 would be a comprimise between 'all-out-litz' and solid core, would involve a wind or 2 more if using 3 strands though.