It just sounds like he is scared being in a new place, not anything to do with you. He has been at the pet shop for quite a while hasn't he? So that was really home to him and all he was used to, even if it wasn't so great. I would go ahead and use what works for him. If food works, then use it to help bring him around. Don't over do the veggies yet, but you can give small amounts of a veggie, like the romaine, several times during the day, then if you aren't seeing any soft poop after a day or two, you can start to gradually increase the amount you give at each feeding. Also I don't know if you tried the suggestion of the blanket over the cage, but I think that would help with his security a lot as well. Or even better, if you have a room that is more quiet and you can restrict your other pets from going in, it might help him to be in there until he has adjusted a little more to his new home, and isn't as nervous. Rabbits that aren't used to being around cats and dogs, can sometimes be very frightened of them, even petrified to the point of injuring themselves. I know some of my rabbits freak out if they see a cat or dog, or even smell it from me petting one. He may just have a hard time adjusting to the other pets in the house and may need a more gradual introduction to them, once he has settled in and is feeling more comfortable. Remember to him, they are the predators and he is the prey, at least until he is able to realize differently. It could be a big part of his distant behavior and hiding all of the time.
I think bringing him out of the cage now, may help as well. I think a good way to do it would be to bring him into a bathroom or other small quiet room, and just sit in there with him and let him play and explore. You could bring a few toys and boxes for him to play with. Usually when you do this type of play time with a new rabbit, you would just sit in there with them and basically ignore him while you read or do stuff on your laptop(fyi- rabbits LOVE to chew power cords). But it really depends on the rabbit. If he approaches you and is interested in you then petting is ok, but if he seems a little skittish and scurries away when you reach out, then just ignore and let him play for a while. Once he starts feeling more comfortable with his new home, then he'll probably start approaching you more and be more interested, then you can start reaching out to see if he wants to be petted, but usually when they are running around playing, they only want to be petted when they flop down and are tired. I think letting him have this play time may help him realize that this new place isn't so bad.
It's possible the whistling noise you are hearing is from him breathing fast because he is nervous. Otherwise it's just something to keep an eye on. Also keep an eye on the water and food levels to make sure he is still eating and drinking. If he's drinking, then he's got to be peeing somewhere, maybe inside the igloo?