I have the exact same issue with my player; the disc clamp is broken, missing a flange holder.
But also the disc tray is badly affected (won't open and close properly) by a rotten motor (I guess).
Anyway, even if it would work I still find the Denon DCD-1500MKII player's sound anemic, congested, restricted, reserved, unclear, lacking in all aspects of naturalism, musicality, definition, and overall involvement. ...1987 wasn't a good year for CD players, including this one.
And the entire disc transport is simply pathetic (wrong spring tension, loose belt, burning plastic, etc.)
Today you can get a much better CD player for almost nothing. ...Or a turntable (for less money) that plays LPs with much more life. The Denon's sound I find it dead.
Glad you now got two operational players. Enjoy them for what they truly are.
And no matter how you cut it, compare its sound with another much cheaper and not so old player for a reality check.
What's the use to have a tank if it doesn't travel fast enough, and doesn't focus on its target with accuracy (wrong caliber shells).