Dog resource guards rubbish he picks up in the street, what should I do?

I recently adopted a rescue cavapoo who's got a resource guarding problem.

He's been known to do it on things that are fairly manageable, such as the post if it comes through the letterbox, cardboard and chews.

However he sometimes steals, as there are rooms we don't allow him in, and if he gets in there he pretty much always finds something to guard.

He's also on occasion decided to guard an ornament that he previously had no interest in, which makes us worry about ever leaving him in the house outside of his crate, which we'd like to be able to do.

When he does this he's a bit of a nightmare, as he'll bark when you leave him alone but if you enter the room he'll growl at you. I don't know what the heck he wants.

He also occasionally guards bits of trash that he finds on his walks, mostly crisp packets and tin foil, which can be dangerous.

I'm really concerned with this, as I'm worried that if we ever leave him at doggy day cares or with family, he'd potentially bite them if he takes anything from them. Furthermore, we can't really let him off the lead, as there's pretty much always a piece of trash somewhere. He gets angry eyes when he does it too, we can tell when he's changed.

My difficulty is that I've found that there are contradictory pieces of advice when it comes to dealing with this.

The rescue said that he's likely to stop this when he's settled, and it's a reaction to stress, but we've had him for over 3 months and he still does it. They said that he may stop when he realises that we don't take, only give, but we're convinced by this point that's not going to naturally occur.

The main pieces of contradictory advice is:

1: if a dog is guarding, teach swap. Offer the new resource. He should be ok to leave the other one (this was mostly from MK9Plus)

2: if a dog is guarding, wear some tough gloves, take the item, immediately give the dog his high value replacement reward and give praise (what I understand from the Mine! book). This way seems very dangerous and might encourage him to stop.

Given how well trained he is after getting him from the rescue, I'm beginning to think that it may be a lost cause, and the previous owner just didn't tell the rescue how bad of an issue it is to avoid him being put down