I use a chunk of brass ( A brass drift) about 4-5" long. Brass being softer than the Sprocket, you can place the end of the drift against a tooth, give it a good whack or too, then make your way round the sprocket every 2-3 teeth. This helps break any alloying or adhesions that seems to build up, or just sheer torqued-on tightness. Then wrap and old chin round it, clamp that in the vice as if you were clamping the sproket in the vice to turn the wheel, but with the chain to protect the teeth, then get you and a Mate to give it a good heeve-ho in the right direction and it should unscrew. I went through Heaps of sprokets too before I found this method. Used to cut them off or trash them with Huge industrial size pipe-wrench on it, which still didnt get it off.
IveTried heating it up, that just made the spokes weak having changed the metalurgy, tried splitting it off like nut splitting, that just f**ked the Hub. I Tried a big bar through the cut-out in the rim, that bend the bar and made the rim look shit.
Try the brass drift ( with the Tyres on and pumped-up so you can hit it whilst the wheel is on the floor/bench, then clamp it as Mark W's photos still with the tyre on for something to hold and twist it.
Make sure you put plenty grease on the threads before putting the sprocket back on.