So, it was only a 10 min CN? I would think 1:45 pm might have actually been a bit too late, then. Or, if that was a typo, and it was 20 min, I don't think putting down at 2 pm is too late, really, as you can wake him at 3:30 pm and still do bed at 7:30 pm.
It is a tough call, though, when bedtime starts to get too late. You just need to decide what's best for your family: the shorter one nap and earlier bedtime or the two naps with later bedtime. Of course, you can always cut the CN shorter and put down earlier for the pm nap. After a 10/15 min CN, I'd go for a middle A of 2 - 2.5 hrs.
In terms of the lovey throwing, I'd just leave him to it, unless he starts to get really upset. Then you can do a type of WIWO and only retrieve the lovey every few times or so.