I've never heard of that injection idea but I do not lay glue-downs on a regular basis. Sounds funky.
Your floor is uneven, level wouldn't matter for the flooring.
If the dips are less than an inch a floor leveler would be the option I would use. It can be feathered out and give you an even floor. There may be very high spots though, that you do not want to fill to so you may have some concrete removal too.
The floor needs to be very even for glue-down and if you do level the floor make sure it has dried completely.

What they plan on doing is not usual practice. Flat to within the flooring manufacturer's specs is what you want. Any competent floor person ought to be able to do that. Flattening concrete may not be cheap, but neither is the epoxy repair material they propose to use to "fix" any problems with the job. Sounds like they want to do as much flooring as they can in the least amount of time...that is just ONE thing wrong with the flooring business today.

Look for other floor people or subcontract that part of the job.

Glennsfc, what type of leveling compound should be used?

A cementitious (aka cementious) self-leveling flooring underlayment, such as that manufactured by Ardex, Mapei or others. It must be installed over the correct primer. Leave out the primer and your money is wasted and so is the flooring.

Glennsfc, is this hard to do? I have access to a 10' aluminum straight edge and have finished a little concrete in my time. I would assume the process would involve marking the areas that are more than 1/8" low in any 10 foot length (floor spec), prime and fill with the compound. I would overlap the straight edge 5 feet as I move across the floor. Is this compound sticky? Can you screed it with the straight edge? I actually thought of pouring water unto the floor to reveal the bird baths then outline, shop vac the water, let dry and fill per directions.

Any cementious floor filler will be 'sticky' to a certain degree. The least expensive would be a product such as Ardex Feather Finish or Mapei Planipatch. Both of these require no primer and are placed on the floor and then screeded. The Planipatch can be mixed with an additive when going over a surface that has adhesive residue or when going over terrazzo, VCT tile and some other situations.

Self-leveler is more expensive and requires a primer. The advantage to the self-leveler is less work in screeding the product. Otherwise, either system works well.

Your idea of using water to reveal the bird baths is clever.

You will have to determine whether your concrete is ready for filling. Mapei, Ardex and others have recommendations for moisture emission limits and such. Lots of good technical information at the websites. Just google Mapei or Ardex for addresses to their sites.

I like your water reveal method and I plan to use that idea on my next job. However, moving around the slab with a straight edge and a permanent marker to mark out the low spots is fine too; that's how I do it.

Something like Ardex K15 can be installed to a feather edge, so you can just fill the bird baths. If your slab is good to begin with, just filling the bird baths (low spots) is all you need to do.

Are the permanent marker lines still visible after the Ardex primer has cured?

When you try the bird bath idea, will you use Ardex or something else? Do you anticipate a delay for drying time after removing the water? Let me know how it works.

K15 primer will dry clear, so you will be able to see the marker lines.

Water will flash off the concrete quickly enough. Ardex primer can go over damp concrete. When it is thoroughly dry, the fill material can be placed.

I usually just use Mapei's Planipatch...similar to Ardex Feather Finish (aka under the brand names Henry's or Armstrong). Using that eliminates the need for primer. As I explained before...it just requires a little more work to screed and smooth, than the self leveling products.

Looked at Ardex products and now see that they produce both the FE and SL materials. Thought they made the SL only. Thanks for all the info and would like to know how the water method works. The only issue I see is needing some old towels/blankets or tarps rolled up to protect the baseboards and to dam the water.

I'm not pushing you to use the water method to help mark bird baths, as straight edge and marker will do the job well enough. However, that said, should you choose to do the water method, adding just a few drops of food coloring to the container of water will help you see where the bird bath 'edges' are.

I would think that knowing where the lowest spot is and slowly pouring the liquid until it is flush with the surrounding area will reveal the edges of the bird bath. This is new territory here...I know of no one in the industry who uses this proposed method to reveal the edges of bird baths, but it seems reasonable to me. Of course, once I attempt it, I may declare..."What was I thinking!" LOL

BTW, we use self-adhesive closed cell urethane foam strips to dam pourable products to keep them from migrating where we don't want them to. You can purchase these at any hardware store or big box retailer. It is simple weatherstripping.

Best of luck with your floors.