I pack some old fire hose, 12" lengths, plus some conveyor belting, to use as softeners for my slings. But I would also use, in a case like that gen set that got dropped, some scrap lumber to keep away from that flange. Better yet, a spreader bar, but then you better have the CG figured.
I was picking a 12 K CAT gen set for the city a few years back, and the CG on the thing was unknown and NOT where we thought (no rigging info). We (the city boys and I, mostly them, and I made it clear it was their call) figured best we could and I picked it 6" above the ground, and stopped. They all looked at me and I said "let's give it a moment or so...", I only had to go over a 6' wall with it. I used the wait time to ask them exactly where they wanted it, just killing time really. About 45 seconds later, without anything moving, the generator shifted out of the rigging, not hurting it or anything. If memory serves me. I think the thing had the fuel tank on top, with fuel in it, or something weird like that, I've picked them before and after and never came across one like it since. Since then, I've used that "wait a minute" thing a few times whenever things are getting a little strange.
The worst thing about getting totally dialed into any activity, is complacency. I fight that all the time flying, and now craning. The better and more experienced you get, the bigger danger complacency is, and it never goes away! I constantly tell myself "you're getting paid by the hour" that seems to help me in doing it safe as possible.