Honestly I don't know why red and tacky wouldn't be a good grease to use for the centering ball. I honestly think whoever told you that might not have known exactly what they were talking about. That's the nice way of saying I think they are full of shit.
But I also don't claim to be an expert on grease. But we've asked an expert on grease what type of grease we should be using for this particular application. The answer was to use a grease with a calcium sulfonate additive. I don't know why or what calcium sulfonate does, but the guy seemed to know what he was talking about so I trust him. Also, this was an experienced person at a grease company, not just some kid behind the counter at O'Reilly's. We currently use Dynalife 220 #2. Before that we used Prolong brand grease, also with calcium sulfonate. The only reason we switched from prolong to Dynalife is supply shortages. We couldn't get Prolong for something like 6 months or more. I found an insightful explanation on the internet. It looks like lithium grease (red and tacky) is best for heat and calcium sulfonate, though still has a high heat rating, does best for load life.
https://www.bellperformance.com/bel...lfonate-grease-the-workhorses-of-the-industry