For a wound like that, I would stay with the neosporin, probably for a week or so, maybe more. The gentian violet is more to cover a small wound to keep a bird in the flock and let her heal. You're going to have to keep this one separate for several days or they will just keep reopening it...
You'd be surprised how resilient chickens are. Clean up the wound with a little soapy water, or whatever you prefer, and put some Neosporin or other topical antibiotic. The only cation is, never use anything that contains a "caine" drug such as cetacaine or benzocaine.
The main thing is to...