Concrete – options for new floor over concrete slab

I am in the middle of a basement renovation, roughly 1000 sq feet. The existing floor is some sort of vinyl sheet material over concrete slab. There is an existing floor drain in the current washing machine room. I am planning on moving the washer/dryer, and have cut the slab for the new drain line, but was not planning on removing enough of the slab to add a new sloped floor drain. I would like the room with the existing floor drain to end up with a level floor.

Some areas of the vinyl were in poor repair, delaminating, or cracking, some were in good condition. Initially I thought I would simply scrape up all the old vinyl sheet material and then use a self leveling concrete (SLC) to fill in the slope near the existing floor drain (not sure whether to cap or plug the pipe and seal it in, or just extend it so I have a drain w/ no slope toward it?).

However now that I have started scraping the vinyl, I am not so sure. Some areas came up pretty easy, but left quite a bit of adhesive and paper-like backing material. Other areas feel more like chipping concrete. I have tried boiling water, and this helps a little bit but I am still not able to scrap down to smooth, bare concrete in most places. I think doing the remaining floor might take weeks of labor.

I am not certain about what finished floor I might use yet. Likely tile in about 1/3 of the area and floating laminate in the rest.

• Are there any other tricks for scraping up old vinyl and adhesives? (I am not too keen on solvents because I have heard they can soak into the slab and make it difficult to bond anything later, and I don't generally like working with chemicals if I can avoid it).
• How much of the adhesive and paper backing do I need to remove? Everything down to bare concrete? Or will the SLC work over stubborn patches of paper/adhesive.
• Is it possible or advisable to simply remove all the vinyl where it is poorly bonded and then pour SLC over the top of the rest of it? Would that be really expensive for 1000 sq feet?
• Is there some completely different solution here that I have not thought of?