I think you will find the problem is that the pipe has lost flexibility because it is blocked. I assume your holding tank is in the cockpit locker so you have pipes both going out to the tank and coming back to the seacock. If that is the case, both will need replacing and you might have to bite the bullet and cut the pipes at the toilet and holding tank end and remove both of these to give you room to work around the ends of the hoses, Obviously remove from the seacock as well. In theory the pipes should then just pull through - that is the way they were installed, but the lack of flex will make it a struggle. This will also give you a chance to clean the tank thoroughly. Also worth replacing the outlet seacock and fittings with DZR items.
Use Butyl sanitation hose for replacement as this is more flexible and less prone to leaks and smells. The calcification is caused by urine being left in the system. To minimise this always pump enough seawater through after using to clear the pipe to the tank - 12 pumps minimum. Avoid leaving waste in the tank for any length of time. When you leave the boat pump freshwater through the system so there is no urine/seawater mix left and leave the outlet seacock open.
Horrible job ahead of you, but if you follow the advice it will be the last time you have to do it. Don't forget to pass a spell on the errant previous owner for allowing it to get in this state.