Does the game check how many runs you have been through gauntlet mode?, can you get the ultimate only characters without running through Dongkou DLC stage?

Your best bet is to run stages were miasma is really low. Bonds item usually drops from miasma up to 25. Higher than that and the chances are really low, so you'll need to keep grinding.

I had issues with Kasumi, the last one I was missing. Had to run again and again and again to get lucky to get her bond on a 75+ miasma stage. I did end up with way too many materials for her X weapon though lol

apparently for the Ultimate exclusive character they won't "spawn" as a fixed famous officer in Gauntlet mode until you actually acquire them in the story -_- so this goes for Kasumi, Sophitia, Tamamo, Kyuubi, and Sterk. Kasumi now spawns in Gauntlet mode after I acquired her and the Camp is upgraded, so for further sanity checking I'm now checking Gauntlet mode everytime the camp has changed

for tier 1-2 camp (IE the best you can do is 2 feasts in the tea house) your defauly spawn is the "basic" WO cast so all the SW and DW cast and the Mystic folks outside of Human Nezha, Kyuubi and Tamamo.

you can however VERY RARELY meet them as part of an invader crew during gauntlet mode