Own a 2001 7.3L that will burn out if left running for more than a few hours or overnight; the video shows how barely the truck makes it through, which was unexpected. I am thinking that the HPOP is failing.
Glow plugs, glow plug relay, and no check engine lights are all new. ICP is fresh. Every liquid and filter, including engine oil, is kept in good condition. The HPOP reservoir is always at least halfway filled with oil.
It seems like it might be starving for something. The fuel pickup in the tank is notorious for causing issues. You should drop the tank, clear the fuel line, and replace the likely damaged plastic component.
Have you replaced the gasoline filter? It seems like it is running out of fuel. Begin with a basic step. It doesn’t take much dirt to clog those lines, so if the gasoline filters have been changed, drop the tank and check for it.