Right outside my front door is a 'entryway' or 'landing' which is a 12' x 5.5' concerete slab. The edges of the 'landing' are slate slabs ~1' wide. 5 steps lead down from the landing to ground level. As you walk up, you first step onto the top slate edge and then on to the concrete slab. The builder did a bad job job compacting under the slab. As a result, the slab has sunk ~1.75 in but the slate edges have not sunk. The ~1.75in gap between slate and concrete slab has become a tripping hazard.

The house is in NJ with winter snow and freezing.
I've been told that the 'correct' way would be to remove the old slab, put more gravel, compact, and pour another slab. This is very expensive and it might sink again. I do not want to go that route. I am thinking about putting pavers over the existing concrete slab - so I can do it myself. If it sinks in few years, I can raise the pavers by putting more sand/granite dust underneath and resetting them. I have several questions.
1) Is it OK to put pavers in front entryway? I've rarely see pavers in the front entryway - most homes have concrete slab. Is there a reason for this?
2) Since the gap between slate front edge and slab is ~1.75in, I need thin pavers ~1-1/2 in or less -do they make these? Anything thicker will stick out from the slate edge and will be a tripping hazard.
3) If I can not find thin pavers, I'll have to use 2 in thick concrete squares but these will stick out ~1/4 to 1/2 in. Is there a way to smooth this projection at the edges by beweling with caulk/compound/cement to reduce the tripping hazard.
4) Since I may have to raise and reset the pavers in the future, what is the best way to set them on concrete?
5) Should I put some expansion joint/compound where the pavers meet the slate edges to allow for expansion/contraction?
Thank you very much for your help.
This thread is great - I found answers to some of my questions.