Umm, I don't know a huge amount about it, just my experience really. If you search the forum there's a long thread about Victoza in the meds section.
That said, I think the reason it's not licensed for T1s is exactly the fact that we have no insulin to stimulate. But Victoza has another aspect to it - it stimulates the release of whatever chemical it is that gets produced when you're eating and you feel full. Basically it makes you feel full much quicker, after having eaten only a small amount. And it generally reduces the appetite. It also allows you to reduce the amount of insulin you take. Im on the basal bolus regime too and because of insulin resistance I was on a fairly high dose, though not as much as the OP - 80u basal a day and 2u bolus per 10g of CHO. That's reduced to 56u basal and 1u bolus per 10g CHO. Since high insulin levels encourage weight gain, this has also helped me to lose weight, along with the reduction of appetite and the feeling full thing. I've lost 2stone, down to a size 14/16 now. The side effects when I first started were HORRIBLE!! I was ill for two months. But I'm so glad I stuck with it.
My diabetic consultant suggested I try it but it is down to a GP to decide whether they'll actually prescribe it for you. It's expensive, I think, and not all surgeries will agree to do it for T1s.