Wouldn't bother wasting your time talking to O2, they may tell you what you want to hear but in reality their service uses long lease IP addresses.
I often go away from home for days at a time and generally switch off my electronic gear when away to save power - not once did I find that even after a couple of days away my IP had changed from the one I was first given.
Maybe I just had an unusual case but a read around would suggest that you need to leave the router powered off for days not hours to get it to change.
FWIW changing your routers WAN port MAC address on Be/O2 would result in you getting no connection for a few minutes as they record your MAC address and tie it to your line for a short period of time during which it won't issue a connection to any other device.
I wasn't suggesting that a dynamic IP was linked to a poor quality of service, what I was implying is that the majority of ISPs these days are using "sticky" IP addressing or just giving you a static one as default.
Yes by all means your customer is the most important thing, but if they are saying they want it this way for security (and for whatever reason you don't want to explain specifics - fair enough, its not our business) you may want to educate them a little bit and explain that a dynamic IP gives them little to no protection.
Cost is not important to you in this case so I'd talk to a proper business ISP such as Zen, or A&AISP and explain to them what you want and probably why you need a truely dynamic IP address and they will more than likely be able to sort you out with something.