Three ideas.
Pile the surplus soil and clay dug out from the moat onto the right hand side of it to serve as an impromptu wall instead of using logs, and try flattening the soil walls when this is done to make them sheer, preventing the slimes/anything else from vaulting over them as easily as the logs. Since the logs work as an adequate - albeit crude - weapon against the slimes, roll them a small distance behind the soil mounds so they can be used to repel any slimes that return (after all, if we keep the logs right next to the moat and attempt to use them to squash the slimes again, all we'll end up doing is pushing the logs into the moat, providing a nice little walkway for anything that would like to cross).
Stockpile the bricks/broken stones in/around the shelter and campfire. Projectiles of any kind with a bit more blunt force behind them would be more useful than the spears, considering how resistant the slimes are to piercing weapons and how quickly they could be thrown even by some untrained peasant as opposed to the accuracy required for throwing a spear. We're also indulging in a great ol' bit of wishful thinking if we think stick-men and slimes were all we we're going to need to worry about (I mean, hell, how do we even know those are BIRD eggs? And even if they are, what KIND of bird? For all we know some slobbering monstrosity could emerge from them as easily as from the damn trees in the back garden of this hut).
Cast small, useless or surplus twigs or branches in a perimeter around the shelter*, to warn us in case anything attempts to approach that Lincoln isn't kind enough to draw several turns before it even becomes a threat. I daresay we cannot rely on the kindness of the artist forever, and forewarned is forearmed.
Also, for the love of God, get rid of those trees to the right of the hut before any others. Burn 'em if we have to. Hell, I'd prefer it if they were burned. There's always the possibility that the stick-men can walk out of trees that have already been cut down, too.
* Just noticed that this may have been a bit unclear. This is supposing that, if something were to approach the camp on foot, the noise it would make stomping through the twigs and branches could serve to alert us. Not only of approaching enemies at night, but of anyone (or anything) approaching during the day.