Im sure i posted about this somewhere else so im just gonna make a list
-backsweetening with unfermetable sugars like stevia
-letting the ferment run its course until the yeast dies
-filtering
-cold crashing. Unreliable if used alone, generally after you add sulphites but if you do it for a long time and rack, then cold crash again it might do the trick
-blending. Make a dry mead. Make an ubersweet mead by starting at a high abv and adding more and more honey until the yeast gives up. Then after racking and clearing both of them, blend them.
-fortification. (This just ocurred to me, dont know if someone tried) Add honey to get your yeast to 14-16%. When it gets to 10%, cold crash, rack, and add some 95% neutral alcohol until you get your desired abv. The alcohol and the cold crashing can do the job.
-clearing. Maybe if you ferment your mead dry, let it clear, fine it with something that precipitates yeast and age it to make sure no yeast is still there, maaaybe you can backsweeten and it wont referment.
Also, I also wanted to do a sulphite free sweet mead, so im starting a batch in early-mid march and i will tinker a bit with it. If i get good results i'll let you know.
And, just as a question, are you sure its the sulphites that cause your hangovers? Im just saying because they get a bad rep but it might be something else you know... Grape tannins, sorbate, or just low alcohol tolerance.