Couple items on John Jackson (he never recorded under his name)...
From an interview with Jay McShann (http://www.tonyspage.com/jay_mcshann_visits.htm):
''"At one time, Bird came to me and said, 'Man, this John Jackson (the other alto player) is readin’ rings around me.' We had a lot of new music at the time. He says, 'I gotta go in the woodshed for a couple of days. And when I come out the woodshed, if I don't cut that stuff by sight, you can fine me.' Bird came out and Bird cut it better than anybody."
The Jay McShann sax section in 1941. John Jackson is supposed to be the alto player next to Parker.