This is also no incense, but technically I've used Stamina Incenses on my Gogmagog and I didn't want to give a false impression. This setup works entirely without incenses, you can try it yourself if you don't believe me.
Strategy:
To start, Nahobino uses Lunation Flux to pass to Nahobeeho, who uses Omagatoki: Strategize.
From here, Nahobeeho and Mastema switch back and forth between themselves, Azazel, and Tzitzimitl to get everyone to -2 attack and agility (NOT Belial, as defense increase will make sacrifices survive their own attacks). Afterward, Amanozako is swapped in to switch ally debuffs to buffs. (Belial can be swapped in a couple times after Amanozako to make the sacrifices die to their own attacks a little more consistently, but I never found it necessary.)
Next, physical sacrifices are brought in and immediately use Critical Wave to kill themselves. Once a couple flashing Press Turn Icons have built up, Nahobino uses Evergreen Dance to assist in building the Magatsuhi gauge to full.
Once the Magatsuhi gauge is full and there's still Press Turn Icons remaining, Arahabaki uses Impaler's Animus, and Azazel, Belilal, Tzitzimitl, and Amanozako are switched in and out to fully buff at this point, because the defense debuff is now necessary.
Then, Xiezhai and Gogmagog are switched in to get a couple Figment Slashes off. Gogmagog is always switched out and back in between attacks to refresh Impaler's Animus.
When there's only one flashing Press Turn Icon left, Xiezhai or Gogmagog is switched out to put in Dagda, who uses Dana's Wisdom to refresh the Press Turn Icons.
Lastly, Xiezhai and Gogmagog are put back in to finish off Demi-Fiend with Gogmagog's Figment Slashes. As before, Gogmagog is switched out and back in between attacks to refresh Impaler's Animus. (Note: I used Stamina Incenses on my Gogmagog, but there's an extra turn here to use a Chakra Pot on Gogmagog to refill its MP, so this strategy does not need incenses.)
Build summary:
Nahobino: Any stats, Xiezhai essence. Null Phys, Lunation Flux, Evergreen Dance
Arahabaki: Impaler's Animus
Gogmagog: Figment Slash, Phys Pleroma, High Phys Pleroma, Critical Zealot, Dragon Eye
Nahobeeho: Null Phys
Mastema: Endure
Physical sacrifices: Critical Wave, Safeguard, Dragon Eye, Bloody Glee, Murderous Glee
All others that are used: Anything
The details for the nerds:
The Nahobino himself is a relatively unimportant portion of this strategy, only needing to carry Null Phys to avoid getting killed/sealed by Javelin Rain, Lunation Flux to save a half Press Turn Icon at the start of the fight, and Evergreen Dance to refill the Magatsuhi Gauge a bit.
Arahabaki is the focal point of this strategy. His passive, Affable Hospitality, grants any ally that switches in the same buffs that Arahabaki himself has, including Omagatoki effects and charge effects. This, combined with Omagatoki: Strategize, allows for repeated use of fully buffed attacks without spending any extra turns doing so.
Gogmagog is used for its passive, Vengeful Might, which gives boosted critical damage per weakness on the active party. Nahobino uses Xiezhai essence (7 weaknesses), Xiezhai is in the party (7 weaknesses), Gogmagog itself has 5 weaknesses, and Arahabaki has 4 weaknesses, for a total of 23 weaknesses across the entire party.
Nahobeeho is used for his passive, Magatsuhi Thriftiness, which reduces the Magatsuhi used by Magatsuhi skills slightly.
Mastema provides an extra +1 press turn thanks to his passive, Crime and Punishment, which activates whenever an enemy hits his weakness or critically hits him. Beyond the physical sacrifices, this is the only RNG-reliant portion of this strategy.
Xiezhai also provides a useful passive in Helmsman, which makes hitting Figment Slash 100% consistent.
Azazel, Belial, and Tzitzimitl lower attack, defense, and agility for everyone except themselves, respectively. Amanozako is used to flip these debuffs into buffs for the party.
Danu and Dagda are used for their unique Magatsuhi Skill, Dana's Wisdom, which resets the Press Turn Icons of the party to how they were when the turn started. This generates an extra four full Press Turn Icons with this team composition.
The physical sacrifices (Yamata-no-Orochi, Garulu, Garuda, and Barong) with Critical Wave are used to activate the Vengeance miracle which gives some Magatsuhi gauge back when they die as a result of their attack getting repelled by Girimekhala. They also critically hit Pixie, which activates the Fell Swoop miracle, which increases the Magatsuhi gauge a little more. These critical hits also give more time to do other actions, including hitting Demi-Fiend with more Figment Slashes.