Setting up new entry-level home theater: Cabling options for projector & sound bar

Hi all,

Setting up a new entry-level home theater which will in basic terms be:

Projector at back of room

Sound bar at front of room

All control & media gear in a cupboard, incl. HDMI switcher

Specifically looking at the cabling options, I've researched the HDMI max distance and am pretty confident I'll come in under the 15m reasonable limit. The issue I may have now is running the audio to the sound bar and back to the projector.

I guess my options are:

Run HDMI out of the 4-way switcher to the sound bar, then double-back another HDMI to the projector--this would result in two 10m+ runs of HDMI; or

Run a 2-way HDMI splitter out the back of the 4-way switcher, one cable to the sound bar, another to the projector--this would result in one 10m+ and one 3m run of HDMI

Use CAT5 converters... this was my original plan, but if I can use HDMI directly, it'll save me a bunch of cash (which I have already spent on a NAS!)

Other info/questions:

Only need 1080p resolution, projector (BenQ W2000) isn't 4K

Would I still be able to use the HDMI CEC features using a switcher and a splitter?

Thanks for your help!