Won't you get fined for tampering if you remove that? I believe it's just the same as opening the box up, they don't give you any more extra cable than you need, unless you expressly ask for it.
Unless you intend to remove it and most likely violate the TOS or call them and ask them for more cable, I think your best bet might be to go buy more cable yourself (which it sounds like you've already done) and buy an adapter/coupling/joiner.
And if I remember correctly, you can also use RCA jacks in the small (digital) box. That might be another possible solution.
