I think with that much movement, I'd go with grease. I only use anti-seize on non-moving parts (threads or the bolts themselves), or a part that moves very little. As an example, I put it on my cush drive rear hub, on the sleeve it moves on. But that only rotates maybe a quarter inch or so .....
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It really needed something there because it was all rusty when I got it and didn't move at all, lol .....
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It came out good and I know it works because it moved as I tightened the sprocket bolts.
Another option may be a grease and anti-seize mix. This was an old BMW mechanic's tip for lubing the splines on the rear drive and clutch. It worked better than any of the several greases BMW recommended over the years (they kept recommending new ones, lol).