Words.
Sentience is experiences. Protein chains and bacteria and even sponges(apparently) and whatnot lack this. They're robots. Input output. Sapience is thought(and yes, language is a side effect), plus reasoning. What we're using right now to discuss this(or should be). Arguably any being that can grasp hefty ideas. Such as ceasing to be in all your entirety, or, possibly, the idea of god. Is sapient. As a side note, apparently some consider chimps sapient, and whether or not it is true it is very interesting.
I assume they(the Trogs) are no better than intelligent canines, or parrots, because we've no idea of their intelligence otherwise, and the chunk of their souls that is missing has to have been removed somewhere- I'm placing my bets on them having animal thought patterns(and have the idea that if we remove that and replace it with devotion, well..). If they're caveman smart, then excellent, we don't have to do much more work in shaping their brains to be built for non-caveman lifestyles.
The reason I suggested making them into new creatures was so they could start again as entirely new beings, with new intelligence and understanding. Instead of having to slave away at teaching the Trogs, we could have intelligent, loyal bug people. Or plant people. Or whatever we mold them into.
Grumugga has had some success with making orcs incredibly loyal. If we can't bind them to us, specifically, we may have to settle with making them enjoy serving under a higher power. Something the knowledge goddess may be able to help us with. Perhaps(one of) the most evil thing(s) to do with the Trogs would be to set up a pleasure loop system into their brain, blissing them into death. Also, they still have free will, as beings with souls, and can be spurned and leave, but lacking 'complete' souls, they'd be harder pressed to do such a thing. The only beings that love(serve) us entirely and unconditionally are our soulless creations. Another evil thing would be completely removing their free will, instead of enticing them to work for us.
Also, we're a young god and just considered something like this. The Empire has probably known about this sort of thing for years, if not decades, or even centuries! The only reason I can consider why they wouldn't do something like this is because of internal disputes(heh), or the fact it'd slash their mana income. They probably don't even need lesser-souled beings to work for them, after all, they're probably loading their people to the gills on propaganda.