They're suggesting two points to strap it down to so it won't flop around. So the goal there really is "don't flap around" not "strap it down", especially if you're avoiding it going into the rear wheel or touching the hot exhaust.
I don't have any good suggestions, only bad ones. If the bags are sufficiently long with a stiff backing, they'll 1) drag on the ground and 2) the swingarm will prevent it from swinging into the wheel. Or if they're sufficiently short, they'll be too short to swing into the wheel (secure those straps though). Short is probably on the safer side. Aside from that, using one of those brackets that bolts to the toolkit mount and risking cracking the bracket seems to be the solution.
Attaching something to the swingarm... I can imagine all kinds of things going wrong, especially if the rider is fat like on my bike. That sounds like a 0/10 idea to me.