I've never known a recycler that wouldn't let you pick stuff out of scrap machines, especially if you're willing to pay them higher than scrap prices! Last time we went to the state surplus auction, I got a grocery bag full of Amperex and Telefunken vacuum tubes out of an old mass spectrometer from the 50's for $5. I became good friends with the scrapper because when he bought a large piece of surplussed lab equipment for $35 (which is what the specrometer went for) I would pay him better-than-scrap to pick pieces out of them /and/ I did the labor myself. So even if there are e-recyclers in your area who just grind everything up, stop by and talk to them if you have the time. Who knows, if they process enough of the right stuff, you might be able to work out a financially advantageous deal for the both of you!
Being friendly with the scrapper got me a lot of good computer deals, too. For instance, he no longer bids against me if there's a shipping pallet of computers up for auction, because I sell him the cases and junk off the pallets for half their scrap value. I get the motherboards, RAM, drives, et c., and don't have to keep bulky generic AT and ATX cases around, and he gets plenty of scrap iron/aluminum for half what he'd have to pay for it otherwise.