I think this would be a reasonable project for an experienced home DIY-er. You'll need an electric hand drill - not battery. And maybe a 3/8" socket with a drive adapter
for your drill. (any good hardware store or Home Despot has the latter)
Do they ship them with the hex head self tapping screws? I just looked at my '74 Argosy stabilizers. The screws are about 3/16" and an inch long and are used with a toothed lock washer. Knowing me, I might predrill a hole with a twist drill if the self tapping screw did not bite well. The stabilizers are heavy -- you'll want to make a cardboard template to mark screw hole locations.
You definitely want 4 stabilizers. Two at the rear and the tongue jack wouldn't be enough -- you'd tend to put too much weight-bearing on the rear stabilizers. And I don't think the tongue jack would take all the rocking very well -- an extended tongue jack would be quite the crowbar! The normal installation is four. When in transit we'll pull into some campgrounds and stay hitched to the truck if the pad is level enough. It definitely rocks too much with the tongue jack down and the BAL stabilizers left up. You are headed in the right direction!
The T-shaped base of the BAL requires two holes 9" apart on the main front-to-back frame. The hole at the bottom of the T is 22" away and intended to screw into the crossways frame member -- I seem to recall it is the main frame part that crosses where the dome ends meet the straight sides. You'll see rivet lines in the belly wrap showing the location the frame structure.
[on edit: get some very good
eye protectors before attempting this.