Why would the E-11 be any kind of development of the E-10? One's a carbine and one's a long rifle; the one is no more a development of the other than an M-4 is a development of an M-16. I've always assumed the two weapons were developed side-by-side, to fill different roles. :/
Anyway, here's another vote for "don't paint it." The developmental prototype is a cool in-universe explanation; another option is that it was a presentation piece - perhaps given as a memento to the engineer that designed the E-11. Whatever story you want to give it, it looks amazing and is decidedly unique.