Hmm the invincible archmage isn't immune to long range magic attacks or magic.. I'm pretty sure he is made ethereal from the cloak, and all magic weapons in BTB count as mundane from gem of saphery or something. This means mundane stuff from anywhere doesn't touch him, and magic attacks in combat become mundane which doesn't touch him. So magic missiles will kill him, Archaon won't. Only problem is static combat res, you get a draw from Archaon and the mage but he still has a bunch of knights chopping whatever you sent in with the mage so you lose. If you sent the mage in alone, well you face at least outnumber and standard so you lose. I can't remember if Archaon causes fear or terror, if he does then you go bye bye.
The null stone is a huge amount of points, and yes it could work pretty damn well to kill him. Bit of a one trick gimmick though, you wouldn't bring it to most games. I have used it once, in a similar way, against VC. Back when my opponent took a really hard VC army, they were new and no one knew how to beat them, and they had won something like 10 games in a row I decided to cheese out (with High Elves?!?! lol) and see if I could bring it down. First turn, moved up. Second turn, flew the dragon behind his GG with vamp lord unit and nicely next to 2 corpse carts, and charged their front with phoenix guard, protected my flank, got chariots and DP in position for next turn and waited. His turn came round, he went to raise the GG I had killed and I revealed the null stone, meaning no magic or magic items work within 6". No invocation, actually basically no magic at all. My turn 3 came, chariots charged in with PG, star dragon charged the rear of the GG providing huge static combat res and lots of kills, whole unit and lord crumbled victory to me.
Tyrion really loses to Archaon most of the time statistically? Tyrion is meant to be better vs characters with his s7 ASF, while Archaon is better against units with the doubling attacks from the sword. Certainly in the old rules Tyrion had an edge, I guess Archaon is supped up (and points halved!) in their current edition though.