Just my opinion. REPLACE IT NOW. You paid for a concrete floor not a skate park. Caps will work but at least three inches and they still aren't right. It's not the strength because the cap will be supported by the original. But I think the problem would be in getting the cap to bond to the old and then the difference in expansion and contraction of two different thicknesses of concrete.
Good luck

No screed? What did he think he was gonna do, "eyeball" it flat?

I'm with newgarageguy. No way am I accepting a hatchet job like that. If he didn't know enough about concrete work to get it flat, what else was done substandard, that isn't as obvious? Tell him the only acceptable fix is a complete tear-out and redo, this time using an experienced sub to manage the pour. Or any other solution that he can propose, that is approved by a PE (Professional Engineer). You pick the engineer, the contractor pays his fee. No PE worth his salt will risk his licence by approving a subxtandard fix.

Get a laser level and document the actual extent of the out-of-level condition, with plenty of pictures. [If the pour was done to standard specs, there should be a slight slope from back to front of the slab, about one quarter inch per foot or so. Bur I know you are saying that there are severe dips that have nothing to do with that.]

The contractor isn't going to be happy about having to fix this properly, because it's going to come out of his profit margin. But he has no business expecting you to live with his mistakes, or underwrite his learning curve.

I'm going through the same problem. I had a garage foundation poured along with what was supposed to be a stenciled patio. The walls are not "flat or level". The contractor told me that is what shims are for. The walls are off level by 1 inch in 8 feet. The overall dimensions are 28 X 42, 28X32 being the garage and the additional 10 feet being a stepped down carport. When it was time to pour, the carport was not stepped down and I had to shovel & rake it out myself. They weren't going to put down wire mesh in the floor (they thought I wouldn't be home when they poured). They lost the pour as it hardened to fast (because they had to wait for the wiremesh to arrive, then it rained when they were done.) I had tarps available but they were too lazy to use them. My new floor is not sloped to the garage doors as required by code, there are areas that puddle water about an inch or so deep, the aggregate is coming up through the surface, and I have more cracks in this new floor than I had in my old garage floor. The back wall is bowed out so much you can see it from thirty feet away. Oh, and I had this same idiot pour my patio. The stenciling is a cross between the riverstone pattern we requested and "VIBRAM SOLES". I have talked to several other contractors and the sentiment is too rip out the garage floor and pour a new slab, about $6000 more. Gotta do it, I'm going to try to get some of my money back but since this guy isn't registered with the state (stupid me) I don't think I'll have very good luck, Oh by the way it was done by JM Concrete of Old Saybrook, CT. Sometimes he goes by John Micoletti, at least that's who I made the check to. Good Luck!

Most concrete contractors have an account with concrete suppliers. The benefit is it allows them to keep their price down. It also helps you save money. An honest contractor will agree to take full payment after the job is completed and you are satisfied. I know a builder and he has really educated me about the tricks many contractors pull. Ask builders you know who they would trust to do their work.

So, dastuge, I'm assuming that you live in Connecticut since you used a CT contractor. So, I must ask you a question regarding something that you said. You stated that it's code to pour the garage floor so that it is sloped out to the doors? Well, my house is 4 years old, and I can tell you that my garage floor does NOT have a slope and has several spots where just the opposite happens. When water gets in, instead of it "leaving"...it heads straight for the dips in the floor that are lower than everything else. Do you think that I have any recourse with the builder?

That sounds horrible! I agree with the others, tear it up and do it right.

Here is a link that might be useful: Garage Floors