Can someone confirm that this is incorrect. My EAI and DA cogs are visibly different in width and general construction.

I had a similar sizing problem between a Suzue hub and a EAI cog. I could only get my lockring on a turn or so with the EAI but could easily fit with the DA. Having my lockring only fit on a turn or so actually roughed up the threads hub and took some delicate work to get the lock ring back on after replacing the cog, so I would suggest not riding on the wheel until you can get your lock ring on correctly.