Front step repair

Girlfriends house had 12" tile on concrete front steps. Long story short water got under them and loosened the tile over the years during the freezing of the brutal winters here.

Last fall we removed the tile and scraped the surface somewhat smooth then I used some fast set mortar mix to smooth it. Mortar mix setup too fast and I didn't get good adhesion now there's a few areas 1/8"-1/4" deep I need to finish before we paint. Need less than 2 gallons to finish the job. Steps cost $4,000 to be replaced so that's not an option, they're still in good shape.
Is there a good outdoor patch available for thin coating applications?
Don't want to use the same mortar mix because it's not quite good enough for the 1/8"-1/4" thickness to finish the job.

I plan on water proofing the horizontal surfaces to help prevent water damage again before painting.

Suggestions?