Hi @RobertG3046
Sounds like your 2nd slab is sinking which is a bit of a concern as to why for one and if you do any releveling work will it keep moving again is the question. 35mm in 50 years well could be worse and I would hope the movement is finished.
So, try to look at why the slab has moved just for your peace of mind.
Yes, floor leveller will work and probably the easiest, but you will need to apply it in 3 stages and let it set cured between stages as floor levellers tend to have maximum thicknesses of approx. 12mm Ie 3x 12 layers is 36mm close to your needs.
The job might look best if the whole room leveled for the final coat taking up the tiles first
Add a nice floor re tile over the top , I would build in a gap or a planned fault line at the slab join in case of more future movement.
Bastion Floor leveller is probably the best bang for buck at $33.54 a bag.
Pebble Crete will work at the deep end but won't flow to a feather edge at the other end and usually will need to be 20mm thick (look at its specifications on each product) to avoid cracking and the entire floor will need the treatment for a uniform finish but that is defiantly do able If you wish.
The sliding door stuck? Is this floor going up or down? Everything will change.
