For backing paper, try Pacon 57305 Fadeless Art Paper, 48" x 50' roll, Black. You can get it from Amazon or any number of other places fairly cheap. A roll should last a long time.
It is an opaque 20lb paper, like stadard white office paper, black on one side and white on the other. One layer will pass some light but two will not. You cut strips to the same shape and size as a manufactured backing paper and put the black side towards the film and the white side out. You can write frame numbers and whatever else you like on the white side. Put a layer of scotch tape around the ends where they fasten to the spools as the paper is not as strong as regular backing paper and will tear if you don't give some reinforcement but that was the only strength problem I have had.
I have changed homemade several 620 size rolls in room light with no problem. (The emulsion used was a batch of TLF#2 @ ISO ~20.) I had no issues with the red frame number window on the camera but the emulsion was not spectrally sensitized, either. There were no problems with edge fog.