Fold the braid back and over - don't cut it off. Once you have the connector slid over the center foam insulator, lined up and ready to go under the braid and sheath, then put some muscle into it. In a motion similar to breaking a pencil in half (holding the cable and connector between each thumb/forefinger), work it back and forth. You can also put a little twist (rotation) into it. Once you get the hang of it, it should only take about 2 seconds, and just a few back-and-forth motions until the insulator is flush with the shoulder in the F-connector. You'll get the hang of it. Don't try to be delicate - it definitely takes some 'oomph'.
I've got GAS: Gadget Acquisition Syndrome.