If I were going over an old floor with two layers of concrete underlay
sheeting, I wouldn't be that careful about what I was trying to adhere
to as the first layer.
I would certainly clean off all loose and removable debris and
coatings. Some of the latex mastics are quite good, but I would still
go with a solvent based adhesive.
The trick to a good, solid substrate when you have two layers is to
adhere the first layer to the concrete, and the second layer to the
first with plenty of mastic, and a few Tapcon style anchors.
You can make an inch thick solid (near monolithic) subfloor by lapping
your joints properly, adhering properly, and adding a few mechanical
fastners. Installed in this manner, adherence to the concrete is
almost a moot point.
As a matter of fact, in high movement areas of town, when an inch or
so of substrate (board or thickset) is applied under tile, many here
are starting to use a slip sheet method of installation over the
concrete and don't attach the built up material to the concrete at
all. This requires a solid, bondable substrate, but not solid
attachment of same.
I ran into this method about 20 years ago in Houston when remodeling a
house there, and the tile guy I liked put down a sheet of 6 mil, then
built a 1 1/2" mud bed over the plastic. The floor never cracked or
moved where you could see it. Two neighbors remodeling at the same
time were informed that "it wasn't necessary" to put a slip sheet in,
and their tile cracked within a year. The cracking was blamed on slab
movement ( no... really?) and there was no way to hold the tile
contractors directly to blame as he put in the tile as specified in
their respective contracts.
I was last inside that house about 5 years ago, and no cracks in the
floor, even after all these years. That method pretty well accepted
around here now.
As far as tools go, if you see a large tool that would help you zip
through a job, why not rent? We have a lot of rental places around
here that cater to contractors, and they have all kinds of tools. We
even have two Lowe's stores and two HDs that rent tools these days.
And they carry all bits, abrasives, cutters, etc. for the machines
right there in the store, and they don't gouge you when you need to
As always, just my 0.02.