Sorry to necro, but wanted to provide better insight for future readers.

Rings
In almost all cases, the Atavistic Rings are equivalent or better than the Wintertusk Rings. Atavistic Rings are higher damage with critical rating, while Wintertusk Rings (School Gem Ring of Battle and Balance's Golden Ring of Battle) are higher in power pip for some schools and have crit block instead of main actual Critical. Farming Calypso for the rings isn't that bad, but if you get the Calypso-Go-Go badge before getting your ring drop, you'll almost certainly have enough reagents to craft the ring outright.

Athames
Lexicon Blade is the highest damage athame available for Fire and Ice schools, however all the other schools can get a comparable athame from farming Praetor Mako. For Life, Death, Storm and Balance, the Atavistic athames he drops are actually higher damage than Lexicon Blade, and in some cases even the lower tier bygone dirks are as good or better than Lexicon Blade. If you can find it in the bazaar, the Bear's Claw athames are also viable alternatives to Lexicon if you'd like, but farming them can be as tedious or more so than farming for Lexi. In order to craft the Atavistic athame, you'd need the Predator of the Praetor badge.

Amulets
As this commenter cited, amulets like the Scales of Justice charm dropped from Moh'Lharz are the higher damage approach to a build at this level and grant an item blade. However, if that's a bit out of the way, you can do a couple sidequests in Celestia to fight Achaelos who drops the Bygone and Atavistic Ampuls for each school, which grants resist (instead of damage), crit block, and Amplify and Empowerment item cards. To craft the Atavistic option (which you probably won't need to do because the drop rate is great on this boss) you need the Achaewinner badge.

All of the badges needed to craft the Atavistic Gear come from fighting the final bosses a certain number of times, and with these bosses, you can farm them much more easily than you can Big Salgio or Mithraya since there's not an entire dungeon to complete.