There are only two tourniquets approved by the DoD. The CAT-T and the SOFT-T W (wide). No other have passed the tests, and no other has been proven in real world use.
The SWAT-T is better than nothing and has it's uses, but it's not great. It's nice that it can be used for both pressure or a tourniquet, but it's also easy to screw it up.
Having both an Israeli bandage and a CAT-T covers both needs without the negatives of a SWAT-T. Use the pressure dressing when you can, use the Tourniquet if/when the pressure dressing doesn't or won't work. A SWAT-T is nice because it's small and easy to carry. A jack of all trades, master of none.
In this scenario though it really doesn't offer anything over carrying a separate bandage and tourniquet. Are you going to apply it directly on the wound without using any sort of gauze? Also, if the direct pressure turns out not to be enough, you have to remove it and place it proximal to the wound. I'd much rather just leave the pressure dressing and apply a separate tourniquet.
EDIT: I didn't notice the date of this post. I didn't mean to resurrect such a dead thread and there is no delete option.