You have some good suggestions for how to manage the 'I like that one better." problem. For the little boy, how about making a doll quilt, excuse me, a little sleeping bag, with a pouch on the back and put a short handle on it. Put a stuffed animal in the sleeping bag. With the short handle - big enough for his hand, but no possibility or getting his head through it - he will be able to drag it around, and he can put whatever he wants into it.
I made and gave my 4 year old grandson one for his Pikachu stuffed animal. He also got some bowl cozies for beds for his stuffed cats, Pumpkin, Pumpkin and Rock Star. He was thrilled. Me, too.