I'll also assume that "tile" to you means ceramic tiles. There's still some doubt in my mind since you didn't say what type of tiles you want to install. The probable extreme pitch of your floor is another reason for concern.
Those old tiles are probably asphalt tiles, but I can't see how thick they are, or when they were installed. Do you know? Tell us how thick.
Both asphalt and VAT contain asbestos, but it's harmless unless you sand/grind and breathe the particles. You're not doing that. It is considered completely safe to remove the tiles, esp. if you dampen the tiles if they start to break up. There's people who did that for 40 years with no affects. The asbestos warnings were mainly aimed at miners and workers that handled the mineral while it was raw/powdery etc. Shipyard workers, brake pad makers, etc.
The black cutback adhesive may also contain some asbestos, so deal with it without disturbing. You can have both tested if you'd like.
You need to remove the tiles, your plan "A" is not a good one.
SLC would be the wrong type of product even after the tiles are gone. Why? Because it sounds like you old floor is way out of flat, (as was common in those days.) No reason to make a basement flat and level cuz many leaked.
So, let us know your tile plans and might be good to know how flat the floor is when measured with a 10 ft. straight edge. Start with that.