Attachment of electrical box ground bond

I have been replacing some damaged old 2-prong outlets with grounded ones. Fortunately, the house was wired with grounded NM cable and the affected boxes are bonded to the ground wires, but in a possibly unusual way.

The incoming ground is looped 180 degrees around the bonding screw, then about ~2" of remaining wire is twisted around the outgoing ground (a la safety wire). I am putting wire caps on these, but should it be replaced with a separate box bonding pigtail?

Later realized: the boxes are old enough to not have separate grounding screws (there are some extra holes in the box that could be either nail holes or a ground screw hole). The bond is to the set screw on the cable clamp, so on that basis anyway I want to add a pigtail to both the box on a separate green screw and the outlet.

Use grounding clips.

I got dinged by an inspector when I just wrapped the ground around a screw.

What you have there will certainly work. The screw to the metal box will ground it, and the connection to the ground wire going to the next box is good (but putting wire nuts on them is added safety).

Technically, you could just install grounded receptacles without connecting anything to the ground screw – since the 1970’s, all UL listed receptacles are required to have the mounting strap & screws work as a grounding circuit. But that’s a backup – I don’t think any inspector would accept that alone. (But if you tried it with an outlet tester, it would probably show a valid ground connection.) The proper way is to either use the grounding clips Beowolf suggested, or pigtails from the metal box, the receptacle ground screw, and the 2 ground wires, and connect them all together with a wire nut. (The grounding clips can save some space in a tight box.)