I would try OBS as it is cross-platform by nature.
It may not be the right fit licensing wise, so pay attention to this front.
As far as the Official development, C# is not the language of choice used to develop OBS, but there are others out there who have made some headway on this front.
I would recommend GoaLitiuM's C# wrapper re-write "libobs-sharp" as a starting point, as Mono is a part of this user's goals in the effort.
Appended Information
If you are not happy with the progress of the open source community's efforts, you can always download the OBS source yourself, and begin to make your own wrapper(s) as well.
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