Hi and welcome,
indeed, the background database should be consistent with the foreground modeling, especially if it contributes to the final results with a rather high share.
Also, btw., you should not model your foreground system in one process but rather in several ones, as you also say there are several stages. This is typically more clear and also easier to maintain.
In this foreground model, you can of course add credits for by products, that are given to recycling (unless this is rather waste and not a product).
To make your model more consistent, you could switch to the APOS system model then in ecoinvent.