Chaps,
This kind of thing has been around in one guise or another since Pontius was a pilut.
Time for a little lateral thinking. You are up against a serious CYA agency in the ASA (or whatever it's calling itself these days).
The controllers WANT to help, direct tracking gets you out of our patch quicker..then we can go back to reading the book, doing the crossword etc
Try the old chestnut of "for weather avoidance". work out what kind of a turn (or miles off nominal track) is required to get you direct to your desired point. Then call up the controller, ask for 15 degrees left or right, or 10 miles right or left of track to avoid weather... he knows it's twaddle, you know it's twaddle, everyone is legal and happy. You get direct, he gets to give it we all live happily ever after, management can go and tuck their heads up their fundament.
Cheers all.
BTW over here in the ME, direct tracking is given (at least on our side of the fence) in at least 80% of cases.