To me semiweekly sounds like “somewhat” weekly (the same interpretation as in “semiconscious”). With that reading, semiweekly would mean it’s basically weekly but not quite. Maybe it’s not every week, there could be some exceptions.

I like there rationale of using this prefix though. In the same vein, perhaps hemiweekly? Like in hemisphere. Same logic applied but the hemi- prefix is less overloaded.