Stan, I would think there must be a product out there that could be applied to the existing, you need to research concrete products and or speak with someone that is current on the latest materials out there, like the sales rep at the local masonry or commercial building supply house.
Surface preparation of the existing, chipping cleaning, etching, etc. will be one important aspect, the others are bond strength, compressive strength of the new material and abrasion resistance of same.
There are self leveling products out there that are commonly used on precast concrete plank buildings, whereas the individual sections of precast are placed, keyways formed between them, bond beam perimeter is formed, and the entire deck is fully grouted with a 4000 psi flowable grout, which in turn makes the entire deck or floor monolithic, like a poured in place slab or deck typical on structural steel buildings whereas the concrete is placed on Q deck/metal decking and is one slab or monolithic.
On the precast concrete plank jobs there is often times a need to put a leveling coat over the precast deck after it has been grouted, to provide a level sub surface for flooring systems. I did this for a developer on a multi-story high rise building, the material was mixed on the street, sand was the aggregate and it was portland cement based, it was pumped to each floor, was like a slurry and self levelled, thickness was less than 1", it had the bond strength, the floors were cleaned and loose scale chipped off by my laborers. It also had satisfactory compressive strength for the application, but was not suitable for a wear coarse.
There has to be a material that will provide the characteristics you are looking for, bond strength, compressive strength, abrasion resistance and do not forget a non slip surface or finish.
You ought to see how strong the existing slab is, if it is weak,you won't get the bond strength no matter what you use, if it still has good compressive strength, and just a finish issue, then you could also chip it down to a depth that would increase your new material thickness, clean, apply epoxy adhesive and place a portland cement based product with a small or fine aggregate. I would think that there has to be a material out there, it's common problem, we get it in garages, as the salt water from snow and salt in the winter time does a number on concrete finishes in conjunction with vehicle tire abrasion, one side of my garage has exposed aggregate and I've often wondered about re-finishing it with something that would actually hold, no sense in doing it if it will de-laminate.
I like the tile suggestion, just make sure you have a non slip surface, surface prep is done and the thinset or adhesive will bond to your existing, and that there is no danger of freeze thaw cycles becoming a problem if moisture gets under it.