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Sometimes insertion of the torx (works for Phillips too) followed by a tap or two from a hammer to further drive the bit in is of some help. Make sure you don't ruin that which is attached to the screw. The tap from the hammer seats the driver just a tiny bit better and also serves to loosen the screw so that less torque is required.
I like the idea of cutting a slot with a little cutoff tool - never would have considered that myself.
A #6 is a *very* small Torx driver. I doubt anyone has steady enough hands to cut a slot into that :wink: . Slotting also does not work if the screw head is recessed as they often are.
Epoxying would not work too well either, IMO, for the reason that there is too little area for it to grip.
That leaves perhaps the method I had to use recently to undo a #6 torx screw for which I had no driver that small. I got a jewellers flat blade screwdriver and carefully filed the blade so it would jam in an managed to undo the screw without damage to it. It just might work in your case if the torx slot is not too badly mangled. If it is I would try a triangular scraper ( small file ground smooth on all sides) with the tip ground so it just grips the remaining hole. You'd have to push in rather hard as you turn it or you just scrape a neater round hole
If your needing to remove dmaged screws from time to time, check out an auto restoration web site called 'EASTWOODS'. they have some very nice LEFT-HANDED drills that will remove most scres while drilling a hole in the center of the head. Used this set up many time in the field and it works everytime! (drill set is fairly cheap and a good buy!)
This may work in your situation, get a drill bit about the size of the head and maybe some smaller ones and drill it first with a drill bit the size of the head intill you hit the substance the head is aginst (ex. sheetrock screw and sheetrock) then go to a smaller one half the size or 3/4 the size of the first one. you will get the matterial it is holding in place but then the screw will still be anckered in the other object some times you can use vicegrips on the part sticking out to turn it. this is you last resort, what type of screw is it and what type material is it i am not familiar with the item you listed