If you are concerned about the additional forces a 4' Firestik II will put on the mount you may want to consider a 4' Firestik Firefly instead. It is lighter and has more "give" to it than the Firestik II so it may put less bending force on the bracket you purchased.
I have a 4' Firefly and it works quite well - as well as any 4' fiberglass antenna I have used in my jeep over the years. I recommend pairing it with a Firestik heavy duty spring.
You will find some reports on the Internet claiming that the Firefly is more difficult to tune than an Firestik II or that a Firestik II has better performance than a Firefly, or that a Firefly is "too whippy." However, many of these reports are by people who don't know what they are doing, they are simply repeating something they read on the Internet, or they are expressing personal biases without any first hand experience to back them up.
While it is true that if one is seeking the absolute maximum range from their CB installation and one has followed all
the rules for maximizing system performance, then one might
be able to observe slightly greater range from a FS II than a Firefly. However, all Jeep CB installation require compromises in antenna height and mounting location, coax routing, etc. such that most people will not be able to tell the difference and particularly not at the 4 watt legal Tx power limit.
As for being "too whippy," that has not been my experience. A firefly is more flexible than a FS II, but not overly so. A Firefly is nowhere near as whippy as the no longer available K40 Superflex or the Wilson Flex, which I also experimented with before settling on my current antennas (2' FS II for around town and getting in/out of my garage and 4' Firefly for road trips/jeep runs).