My friend has an old Agave Century plant in a relatively inaccessible
location on the side of his house

It's a "century" plant, about 3 feet tall and five feet wide with the
spiky thorns (I don't have a picture, else I would have posted it). Sorry.

He knows I'm now an expert in poison oak, so he had asked me how to get
rid of it. Apparently, today he tried to cut it with a sawsall (leaf by
leaf), and the gooey green stuff made his forearms itch like hell within
minutes.

Looking it up, apparently it has calcium oxalate crystals and some kind
of chemical called a "steroidal glycocide saponin" (whatever that means),
the first of which punctures holes in your cell membranes to allow the
second access to the juicy part of your cells.

(I wonder who is the predator here.)

Anyway, he asked me HOW best to get rid of such plants without getting
splashed with the green itchy gooey stuff.

Any suggestions?