Don't think he had anything to do with Blast First, they were a UK label.
As far as Big Black, Albini was a regular contributor to Forced Exposure.
FE also functioned as a label, one of their releases was a Big Black 7" for FE subscribers only.
FE also assisted labels like Twisted Village and Ecstatic Peace, though that may have been more of Jimmy's thing instead of Byron.
And like others have said, great interview.