The simplest solution is separate connections with a DVI-HDMI adapter/cable, with an Nvidia discrete card (dual audio stream) or Intel iGP.
If you want to go through the amp with one single HDMI connection try an EDID override. This is not so "simple solution" at first, but read through the instructions in my sig. I can help you with the required mod but need the real-time EDID of the proj (don't have the JVC-RS45 in my DB, but other models like the JVC-RS50, which may certainly work for you, but better get the exact EDID of your proj. just in case ...).