Would Jeremy really expect people to believe that Sheila and his parents would leave a loaded gun within reach of two little children?
He seems dumber and dumber. Maybe he is.
Why do you think he said he did it so late in the day? His goal was to try to make it seem that it was so late that they would not notice it and not disturb it.
He wasn't stupid enough to claim he did it early in the day.
It doesn't make him look very good though to claim he did it knowing two young nephews were around so he would have to be stupid to do what he claims he did.
Being that he needed to say he left it out so late in the day he needed to come up with some plausible reason for doing so. The bunny story was the only thing he could think up which wasn't all that good in terms of being likely but he thought was good because it gave an excuse for the magazine being loaded. He claimed they split before he could get a shot off so the magazine was still loaded.
He was stupid in another sense. He didn't count out how many shots he had fired and try to make the number of bullets he staged match his story. He easily could have avoided needing to count the number of shots. All he had to do was take out a full box of ammo and use it so that the remaining number would match his claims. Instead he just used whatever ammo he could from the ammo carrier or wherever then stuck a partially used box with a random number of rounds in the kitchen for his staging. It had too many and thus revealed it was staged.
Maybe he was too stupid to think of using a full box to match his story. But more likely is that he didn't think up the story in advance about the full box of bullets being taken out and rabbits but rather made it up after he killed everyone.