He sounds like a very bright boy and being part Border Collie, I suspect he is bored and has worked out that whining gets your attention, even if it is in a negative way.
Do you do any sort of mental stimulation games with him, as I know BC's can become neurotic and manipulative if their brains aren't utilised? If you gave his brain a good work out a couple of times a day, then he would probably be less likely to try to make his own entertainment.
He sounds like the sort of dog that just running round the park with his mates just isn't enough and to get him to settle he will also need to do some training too. It doesn't really matter what sort of training, just anything where he has to listen to you and THINK. So it could be Obedience, Agility, Heelwork to Music, Search and Retrieve, even just Clicker Training a few Tricks. On top of that in the home you could give him jobs to do...fetching the post, helping you with the washing (passing it to you from the machine), collecting his toys and putting them in the toy box.......With his sort of brain, the sky's the limit really. :wink:
I'm sure once he is getting a mental work out as well as a physical one daily, he'll be much easier to live with and much less demanding.