Re: Crumbling Basement Floors
One thing to think about when considering SLC is how level is the old slab. They are notorious for not being poured level to begin with, and SLC seeks it own (water) level, you could end up not having a controllable situation with the runny cement. If it's very un-level, you might instead consider using a bagged quickcrete stucco mix and troweling it on smooth, level be damned.
Then, to help the new bond to the old crumbling mess, in either case use a masonry bonding agent; a liquid that is rolled on just before you apply the topcoat. It will ensure that the new has some clean surface to stick to.
Remove not the ancient landmark, which your fathers have set.