hot water into cold line

So wondering to be sure on thermospyoning and gravity fed system. Ive got 2 water heaters that are different size. My plan was to just run loop back from the upstairs shower line being the highest and furthest away fixture. But i also have a toilet and vanity and wash machines on basement level...

background- Insufficient hot water coming through shower head (already removed restrictor). It is a Home Depot Glacier Bay one handle valve. The valve has a hot water inlet and a cold water inlet and an up outlet for a shower and a down outlet, which is plugged, for a tub I assume. Removed...