As you joined Aug this year and this is your first post I have to question whether this is a windup?
I am no medic but if you have a history of DVTs as you claim then that would indicate that you have circulation problems not just in your legs.
As such i would guess that you would have problems in other areas which would cause a problem with your class 1.
May I add from a pilot non medical perspective that many people spend as many hours sitting in sedentary jobs or in front of a computer as they do on long haul flights.
DVTs as unique to long haul flights seem a bit of the flavour of the month or a concocted condition which has attached to aviation but which is probably just as likely in your daily work especially stuck in front of a computer.
Now I have got that off my chest have fun and maybe someone who really knows may answer your question.
Pace