4K projector + HDMI switcher?

Can anyone recommend a good 4K projector + HDMI switcher combo for gaming?

I’d like to keep as much of my current setup as possible. Right now I’m using a Samsung TV with four HDMI inputs: one Xbox, one PS5, and one Nvidia Shield, plus one for e-arc to send sound to my 5.1 home theater receiver. With the video signal going directly from the source to the TV, the picture is great as you’d expect. I have not encountered any issues with sound degradation or synchronization with a single device (TV) sitting between the sources and the receiver.

I have yet to find any projector that has four inputs, so a good HDMI switcher would be necessary. I’m a little hesitant to introduce two devices (switcher + projector) between the source and the receiver. Any of you have experience doing this?

This is just the first part of figuring out what it will take to change to a projector setup. The ones I’m finding seem to be designed to be hung, but I’ll be using an existing AV closet with a purpose-built projector shelf at 65” from the floor, and hanging it is not an option. I also have to figure out if the currently unused but still wired center speaker hanging above the opposite wall can be removed and replaced by my (much larger and heavier) center speaker, which may require a custom hanging mount. But first I need to figure out the projector/hdmi issue, since changing configuration would mean having to buy a new receiver with more HDMI ports on top of the other new equipment.