1. At least you agree now, the landlord cannot take the property as his own even if the person committed trespass. So whether it is trespass to put the toy box in the hallway is irrelevant to the issue on hand.
2. Again, finder in most cases could take the abandoned property as his own subject to relevant statutes. However, the prerequisite condition is that the property is in fact abandoned by the owner, not lost. The abondonment status is not determined by the finder's mind, rather it depends on the owner's intent. As the case you provided, the Spanish company won the boat because although it was lost for more than 200 years and they did not have procession or control over the boat for that period, they never have the intent to abandon it. In the current case, the owner placed a box in the hallway before the day he would move in and immediately called the landlord after having found out the box was missing. There is no intent on the owner side to abandon the property. Just like your kid goes to neighnor's house by his bicycle and left the bicycle on the sidewalk without lock. Even though the sidewalk could be the city's property, there is no court would deem the bicycle as abandoned.
If this case proceeds and no party lies in the court, the tenant would prevail. And only possible "defense" the landlord has is to lie about the incident. However, the burden in such case is by proponderence of evidence and if the tenant brings enough evidence, the judge would easily find out the truth.