Improving Unarmed Strike for a Inquisitor or a Zealot

[The Shaman]

Hi, I have been considering making an inquisitor or a zealot of Irori for an upcoming Hell's Rebels campaign (or just a generic campaign if I need a martial investigator sort of character) and link them to the order of archivist, and I have been looking for ways to make them better at fighting barehanded. I thought there would be a feat, inquisition or the like to improve their unarmed damage without relying only on equipment or spells, but I cannot find anything that I can take without multiclassing or houseruling. I am specifically looking for something an inquisitor or zealot can take. So far, my best bet appears to be multiclassing with unchained monk and taking monastic legacy, but I was hoping for something that would require as little multiclassing and come online as quickly as possible.

So far, I have considered the following:

Focused weapon via warpriest or the fighter advanced weapon training - different classes
Monastic legacy - backup option, requires multiclassing or high levels (if taken via ascetic strike)
Lethal Grace - definitely an option if I am going with Zealot, but is it enough?
Fist of the vigilante / Signature weapon - available only to avenger vigilantes. I really want this, but I am not aware if there is any option to take an avenger talent as a non-avenger.
Monk VMC - backup option, the classes I want to play it with do not get a lot of feats.
Greater Unarmed Strike - third party.
Stone fist - spell, thus not always available. Backup option.

Is there anything else?

[Imbicatus]

As a sacred slayer inquisitor, you can take slayer talents. Irori sacred combat ranger combat style allows you to take monastic legacy without meeting prerequisites.

[Imbicatus]

Otherwise, shield gauntlet style will give you increased damage with gauntlets. It's not an unarmed strike, but you can be the man with the iron fists.

[The Shaman]

Wait, wasn't Irori's style the one where you dealt average damage? I did not see anything that lets you take monastic legacy on that feat.

[Imbicatus]

That is irori's divine fighting style, not irori's ranger combat style.

Faithful (Irori) wrote:

Source Inner Sea Combat pg. 11 (Amazon)
If the ranger selects faithful (irori), he can choose from the following list whenever he gains a combat style feat: Improved Grapple, Improved Unarmed Strike, Monastic Legacy, and Two-Weapon Fighting. At 6th level, he adds Improved Trip and Spring Attack to the list. At 10th level, he adds Ki Throw and Stunning Fist to the list.