Early Long Branchs' did have a LB milled front band. See the pictures of such a band on my No 1 Mk VI pictures. Clearly a Long Branch stamp.
I would not go about swapping parts just yet. It is confirmed that Savage and LB swapped parts back and forth, and one could easily infer that they (Savage) helped them get going on the smaller stuff, especially early on.
I'll check my pair tonight for milled or flat bands, as well. One is a re build, one is not. Nice find!