This is how it worked on live, may or may not be the same here. This was a long time ago, so forgive me if I'm slightly inaccurate.
Trooper Mozo is on Legion of Cabilis faction. You will be KoS to start with and you will need to get to dubious to do the bone chip quest. Legion of Cabilis (warrior) faction is easy, just slaughter Sarnak or Kunark Goblins.
The real problem is the Crusaders who patrol right past Trooper Mozo. Quarg and Bodli are not on Legion faction but are on Crusaders of Greenmist (sk) / Scaled Mystics (shaman) faction and it will take many many many bonechips before they will even think about tolerating your dwarven hiney. And they may never decide to do so....
Cabilis has many factions and you can start out at a different level to all of them. You may start off -100pts from dubious on one faction but -1000 from dubious on the next faction. Cabilis factions are also capped and the cap can depend on your race/religon. As an agnostic half-elf bard, I think I maxed at warmly to Legions, amiable to Crusaders, and indifferent to mystics. (not using any illusion or faction song tricks) My Cazic-Thule troll shaman was able to cap higher with Scaled Mystics. A dwarf Brell worshipper is probably going to have different results. I would suspect you may never get to non-kos with the more zealous Cabilis factions (greenscale/mystics) but should be able to be find acceptance amongst the Legions/Residents(merchants)/Swifttails (monks). Just doing the bone chip quest, I maxed out at different times for each faction: Legions first, Residents, Swiftails 3rd, Crusaders 4th, Mystics 5th.
It takes lots and lots and lots of bone chips to max out all factions. Even if you max out all the bone chip factions, you still won't have the run of Cabilis. The Brood of Kotiz (necromancers) will still attack you. This can be raised by killing lots of outcast Iksar (bandits, maraders and such)
It's a LOT of work, but I always enjoyed watching the lizards eyes bug out when I walked past them to bank/sell/quest in Cabilis.
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And yes, I was a bit faction obsessed........lol