The EH 6v6 is a good valve - but that chinese 12Ax7 is a shocker - any good brand will do as a change, but it has to be changed as it is the lowest quality valve I have ever seen/heard.
The Jensen Mod 6 is available from Tube Depot.com - it costs about £20 including shipping -
By the way - have you tried engaging the G12T button on your Session JD10 - I find it compresses the 600 speaker tone so that distortion sounds more real - I also find that with pedals distortion is more crunchy with the volume between 6-7 not flat out. Also putting the amp on the floor in the corner gives it a better bass response. I'll put a new clip in the players section :D