Yup - I'd have wrestled a corn-cob too.
The thing with swapping for treats is that it's only the first step...

Honey can be very possessive of things, and she's not perfect at relinquishing prized items, but we've made a lot of progress.
We started with the swapping for a treat - ideally swapping low value things she had for high value treats! Then we would give a "give" command as she let go of what she had. Meaning we could phase out having the treat there and she would give it up in expectation of a treat. We also did a lot of work on hand-targetting while holding things, so that she would be happy to come to us while holding things without worrying about having to give them up.
Also, in our case, I STOPPED using the "give" command for the one thing she really finds it hard to give, which is a tennis ball, as this was just increasing her resistance (she was associating the command with something really difficult for her to do, and was transferring this reluctance back onto other things).
Now, if she picks something up she shouldn't, she's pretty happy to come to me, so I can see what it is. I fuss her and praise her for it. If it's something she needs to give up but nothing dangerous (normally children's soft toys), I keep fussing for a while, then ask her to give and I find her one of her toys... if it's something she can keep (knowing she'll lose interest pretty quickly) I just keep fussing for a while and then carry on with whatever I was doing. This means that the times I have to immediately take something off her (normally discarded corners of malt-loaf, thanks to my toddler) she is more co-operative.
Other tricks we have used along the way is dropping treats near her, then walking away, so she puts the item down to eat the treat... she normally picks the item back up again, but repeatedly doing this means I can gradually move her away from the item until I can pick it up!! Also, being super-interested in something else (a blade of grass works)... a nosy cocker can't resist checking it out!!!
