Getting a spoke replaced is very cheap at the LBS, sorry I can't remember how much but I was surprised it wasn't more. I've watched experts do the trueing/tensioning by sound (like plucking the strings of a musical instrument

) ... not a skill I have practised. I know I should, as it may be necessary in an emergency when miles from anywhere on tour
You are much more experienced with bike maintenance than I am, so tell me to shut up if you have done the following already

.
DId you check the rest of the wheel carefully, especially the rim near the spoke that broke? Sometimes a broken spoke can be a sign of bigger trouble ahead ... (not from personal experience, but my cousin found several hairline cracks in the wheel of a borrowed bike with a "loose spoke" problem)

It doesn't bear thinking what could have happened if he hadn't spotted it ...
T