Yes, mjpeg is much less efficient than H.264. But streaming through
Blue Iris is also less efficient than streaming directly from the camera.
What I would do is stream directly from the camera. To improve efficiency, I would make these configuration changes:
1) Set the camera to encode H.265. This means no Intel hardware acceleration but it should be worth the tradeoff to keep bandwidth lower.
2) Set the camera to encode VBR at medium quality with a low-ish bit rate limit so that it doesn't use too much internet bandwidth.
3) Set the frame rate of the camera to 15 or less (lower will require less bandwidth).
4) Set the camera's i-frame interval to about 4x the frame rate. i-frames are bandwidth-heavy, but important for stream seeking, so there needs to be a balance.
Then set up a port-forwarding rule for the RTSP port with a source address restriction that prevents anyone else from accessing the forwarded port. To forward the port without this restriction would leave the camera open to hacking, which is not good. If source address restrictions were not available in the router, then I'd set up some other kind of access method such as a proxy server or VPN server running on the BI machine that is local to the camera, and set up the source address restriction for that via Windows Firewall or something.