I can't vouch for it, but there are software mixing solutions. The one I linked to in particular has a very affordable option which sounds perfect for your needs. Have a look around though - I'd be surprised if there weren't a few competitors.
You'll either need a capture card that has mutliple HDMI in, or multiple capture cards - so a reasonably well powered desktop will be needed.
It will still end up working out cheaper than a Tricaster though!