I'm not familiar with your specific Marantz unit, but am familiar with sister Denon, they typically use same processor/menus.
HDMI pass through is usually only available on one HDMI output. The source unit signal will pass-through this HDMI output even when the Marana is turned off. Only pertinent when Marantz unit is turned off.
If you're in the USA, always use NTSC. If you have PAL selected (Marantz or the Sony projector) - it won't work. PAL is for some foreign countries.
You said projector works from laptop connection - are you using the same cable too? If not, check again with same cable to be sure the cable is good (cats, kids, etc.).
Could the 2nd HDMI output be set to a different zone (different source)? This will be selectable from the on-screen menus. Recommend getting it working from a single video source before advancing to different zones to avoid added complication until after confirming it works. Should get same picture on both screens.