Hi Berserker and welcome to the forum.
Just slide off? Rule
#1 of boat mechanics, NOTHING ever just slides off unless it's something that's supposed to stay together.
I would try the usual; soak, heat and beat.
Soak. If you don't have it get a can of PB Blaster or Kroil and soak the shaft hold the damper plate. Get large containers of either of these fluids as they will be your friend in many boat repair jobs. NOTE: Be very, very careful applying either of these around engines and transmissions. They will dissolve rubber or plastic parts
like your transmission
seal. If in doubt spray some in a bottle cap or other small container and apply with a Q-tip.
Heat. After it soaks for a while (longer is better, even overnight if you have time), heat the area. Use a handheld torch (like a propane
torch, not a flashlight if you speak British) if it's safe. Maybe try to remove the part then but often you need to soak again when the part is hot and let it cool. That helps suck more fluid into the stuck joint.
Beat. Well don't exactly beat it but tap it firmly with a hammer or small metal tool. Of course be careful not to mung up any threaded parts
and don't peen over the end of the shaft.
Repeat the steps as necessary and the part will probably come off eventually.
Question, Can you get a gear
puller large enough and will it fit onto the damper? I might give that a try as well but I'm no mechanic
and have not had to pull a plate so maybe wait for expert advice before trying this.