Since the hives come back overnight after having been gone before he goes to bed I'd guess he's allergic to his bedding, clothes, or something in the room. As Katie suggested wash everything in a hypoallergenic detergent without any fabric softener. It will take time to completely eliminate the detergent and fabric softener build up and so you'll need to wait to see if this helps.
Why didn't the allergist do testing? It's true that if it's the detergent they can't tell from a test but food allergies can also cause hives, as can grasses, pollen, chemicals.
Since the hives go away with the Zyrtec and then come back he is still or once more exposed to the allergens. IF he were allergic to the bird seed, you removed the bird seed and anything that has touched the bird seed and have given him Zyrtec and the hives go away but then he gets them again during the night it is probably not the bird seed. However if he has contact with any small dust from the bird seed during the night it might be the bird seed. Did you give him a bath after he played with the bird seed?
It is complicated figuring out allergies. To completely eliminate the possibility that it's the bird seed you ;need to completely remove the seed from the house and clean anywhere that the seed has been so that you're also removing fine dust left behind.
Give him zyrtec immediately when you first notice the hives. It would be a good idea to look in on him during the night. The reason the hives stay longer each time he gets them is that his body is becoming more sensitive to the allergen. If at any time he has difficulty breathing immediately take him to the emergency room. I say this because you say you're expecting big red patchiness in the morning. I had an allergy to bee stings that in one day went from hives to a swollen face and difficulty breathing. ( I was bitten several times.) The hives break out in the airway. I'm not suggesting that this will happen to your son but it's a possibility that you should know about.
I suggest that you write down everything that he has touched, eaten, or been in the area of just before the hives broke out. Over time you'll see a pattern.
My granddaughter has had allergies with asthma and eczema since she was a baby. She outgrew many of them. She has taken both Benedryl and Zyrtec. Her allergist changed her to Zyrtec because it acts in more ways than Benedryl. Also it lasts for 12 hours and I don't think Benedryl does. Zyrtec has not had a negative affect on her personality. Every body has it's own way of reacting. If you haven't had difficulty using the Zyrtec it is the best long term treatment.