Killing the Jewel is impossible, its a fundamental force in the Inuyasha series, maybe if Ainz could erase concepts themselves he could do it but otherwise its like the time stone from marvel. Its possible to fragment the jewel using Kagomes miraculous arrows but breaking it apart any further further than shards simply doesn't work. On top of this, the jewel will always mess with causality so that it is reformed, even if the jewel is sent to another world, taken to the depths of hell, or stuck in a pocket dimension, it will always find its way back.
If destroying was Jewel was actually a method that was feasible the entire show's near 200 episode story would be pointless, the main cast had a black hole attack, dimension slicing blade, Kagomes miraculous arrows, and a variety of highly destructive physical / magical attacks. They would have just destroyed one of the jewel shards permanently so the jewel could never be reformed and problem solved. What actually happens is that the jewel shards cannot be dissolved, cannot be further broken down even with miracles, even if they ended up in a black hole or an alternate reality they will find their way back together. The jewels wish potential is also far superior to Ainz using his wish granting spell, Inuyasha is an isekai similar to Overlord, and kagome using the Jewel could freely wish to go back home or bring her friends with her, Ainz meanwhile using his wish ability cannot even confirm if there are other real life players in his world.
Things in the stone are not immune from destruction as in the Manga the demons were destroyed when Inuyasha slashed the light.
Also it doesn't matter if the Jewel reforms again in 5 years. Ainz only need to finish off Naraku one way or another, destroying he jewel, killing the demons inside etc etc.