Best place to make ticket changes
 

Anyone have any experience of this?

Half way through an AONE5, in the US, and all remaining segments are 'open'.

Is it better to call AA or BA, or call back the original TA in order to book the onwards segments? The bumpf makes it sound like its really easy to book as you go, but gives you no clue how to actually do it!

I would use the TA if I had a good relationship, but otherwise just directly with the airlines since you can easily give them the ticket number. Probably easiest to pick the airline you have best status on assuming that some of the remaining segments are with them.