All good suggestions, but sadly all were tried and failed to reveal
the problem. Gas flows freely through the new gas line; it still
stalls, even running with the gas cap off (seemed like despite all the
other gunk on it, the fuel tank was clean); I have blown out the carb
with cleaner, and all the tiny holes seem to be free of debris (the
ones I could find, that is).

My next step would probably be to replace all the gaskets in the carb
-- assuming that one of them is leaking air and causing the engine to
lose prime. Not sure if that is even remotely resonable though.
Thoughts?

Thanks for everything so far. I wasn't sure (in Telstra's response)
what/where the float valve is, but I am happy to check it ...