I've seen a few different setups for the neckboards on the U5000s and the K7500 (which uses the same neckboard)
the one U5000 I replaced the neckboard on with one I got from a scrap chassis lot actually had a capacitor running from what I believe was the ground on the green drive and running to the CRT ground pin. I wasn't able to get those to solder at the CRT ground pin without the damn pin falling out repeatedly, lol. so I left it off, didn't seem to affect the performance any.
there was another on the K7500 neck that I borrowed for a few months that has a resistor in the heat circuit. the picture looked fine for medium res with my Sportstation, but as soon as I pulled it to use in another cab for Zombie Revenge (which I ran in scaled down mode for standard res) the picture looked absolutely horrible. it was too dark.
the tube on that U5000 inevitably, even after I made my neckboard swap and some other repairs, had a weak red and what appears to be a blue short (I have it turned all the way down and it still has a blue tint)
it's common for these monitors to have major piece of shit Zenith tubes, and typically with a ton of mileage on them.
if you know anyone in the area that has a rejuvenator, I'd go that route first.
otherwise, I have a few more neckboards. one of these days when I start to get caught up more I'll try testing out all those junk chassis I bought and see if any of them actually work.