PrismCast can support more than 1 stream, it's hardware dependent on what your PC can handle (don't try to run on a Synology NAS). Also, there are HBO entries in PrismCast:
And for Discovery, you have to configure PrismCast to enable a screen big enough for 1080 and not just 720, but so long as Discovery is streaming in 1080P on their end, then you should be good (below is a screenshot of Dispatcharr which is what I import all my sources into before sharing with Channels DVR):
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