Pete,
it just sounds like you are having similar problems as the rest of us, an dyes, the seller was bound to hav eknown, regardless of your test drive, as an example, i am having major issues with mine, and all through repairing it this year, i was having little test drives to see if i fixed one issue, seemingly I had, then something else would turn up, anyway, i realised the other day I wasnt drivign it for long enough, or hard enough, for the problems to materialise, hence yourissues turning up after 20 miles of harder driving. these sorts of issues develop, i have found, they dont just turn up. this is probably why the chap has sold the car, hes lucky the test drives went ok.
I don tknow automatics, so dont know what a torque converter is BUT it seems to me that your problem has come about after the engine is properly warmed up, which is what happens to me, jerky jerky then stall. You seriously need to read the codes BEFORE taking to a garage, I bet you have a couple or more codes on there relating to this issue, and I wouldnt be surprised if its the ckp sensor.
reading the codes is not hard or complicated, you just need a paper clip and you can do it from the drivers seat. Get that done FIRST job, and come back to us.
this is bad luck mate, but listen, its worth saving, and with help from us lot, you can keep the costs low I am sure.
I just looked up torque converter, obviously an auto thing, when the cars cooled down, try it a again, go for a "test drive" and keep it local, see if it goes...get those codes read then....