Ok, you need to clarify some things first.
what are you talking about when you say 'personal gear'? Your medical kit?
If you're hangin out by the CP you're useless. You're not a tactical paramedic. You may as well be sitting in your amb - co-located behind the perimter - where the "CP" is. If someone goes down, you are no where near the the element and you have no means to get to them. Maybe if you have a baby sitter to take you to the cas, but then you're entering into an unkown enviroenment.
Unless you are throwing a lot of resources at a call, you're manpower is going to be limited. Typical Tac team is 6 guys. A "CP" probably wont even exist. It will consist of the Tac Tem Leader in the back of the stack, with patrol on the perimeter. You need to be co-located with the element, best to be in the back of the stack, or shadowing the stack. Otherwise you're useless. I think you seriously need to square your tactics away at the same time as sorting your gear out, and by the sounds of it you have some work to do to field an effective resource.
Can you define 'enough kit for a rapid stabilization'? both the kit and what a rapid stabilization is?
Butt Packs are useless - you cant get at them, and you cant rely on anybody to get gear out of one for you either. Your med pack should be left at the door, not at the CP, unless its not a building. A vest is reasonable. Leg rigs are good. You shouldnt need much more than that.
Why dont you start with a list of what you're carrying first and then ask whats the best way to carry it, or is that what you are asking, what is the best kit to carry and where?