Here are my thoughts (and I've worked with a lot of residential and commercial concrete step applications over the last 40+ years, poured my first one in 1969):
You'll save a bundle of $$$ by doing everything yourself. That being, delineate with sawcuts and completely remove the steps. Repour with uniform (treads and risers) reinforced concrete steps, tied into the porch concrete with doweled rebar. After a thorough cure time (28 day minimum), sandblast everything, then apply a textured (thin-bonded), low-modulus epoxy overlay with (broadcast) quartz sand aggregate to all surfaces. It will look decent and not out of place with your house's character, will have tenacious, non-slip characteristics when wet, and will also effectively deal with the existing porch floor cracking.
Total material cost, including rental of a 90-lb electric concrete breaker and sand-blaster, should be well under $2000.