Our being vs. the fact that

Our being feels awkward and unprofessional, to me. This is a situation in which it would be fine to use the fact that, but you could also rearrange the sentence to avoid it and to be more specific. For example:

We are solely distributed in the Greater Detroit area, but that will no longer be a problem when we are more active online.

When we are more active online, it will no longer matter that we are distributed only in the Greater Detroit area.

Personally, I think your original construction using the fact that is fine, but rearranging a sentence to avoid using a phrase you don't like is always a good option!