I agree with Bahamut_A6M5's great suggestion that successive shots be a requirement for the "stun-to-death" effect. I also agree that the save against any ZAT effect should be constitution based (appropriate save is TBD). I would also suggest that ZAT attacks bypass standard forms of armor and that "normal" armor saves do not apply. Since the time-frame of the RPG falls somewhere in Season Six, there may be technology (aka Kull Warrior Armor) that can be obtained in a mission and researched to eventually provide some PLAYER protection against ZAT attacks.
IMHO, the ZAT has the potential to be a very "broken" weapon, and should be "nerfed" for the purposes of the RPG.
Here are my ideas on that:
It may seem a bit contrary to SG Cannon, but I would consider the idea that the the ZAT could be treated as "unwieldy" when used as a fully ranged weapon and suffers from the additional traits: 1. Attempts to use the ZAT beyond melee range do not benefit from "to-hit" modifiers. 2. Using a ZAT is a full round action. For additional balancing of the "death shot", I would also add the requirement that, "for death to occur, the attempted shot must be made at point-blank range". A shot at a range beyond point-blank would result in an slight extension (+1-2 rounds) of the stun effect (or some variation of diminishing returns on successive ranged stuns here). If a PLAYER is stunned by a ZAT and fails to save against a "death shot", then their HP is reduced to zero, which triggers the standard 5th edition "death saves".
Some other traits of the ZAT:
1) It can be used to overload (disable) various "electricity-based" technologies.
2) Stun shots do not cause "damage" to characters.
3) It can still disintegrate "dead" organics. However, (for balance but also contrary to SG Cannon) a single ZAT only has enough power to fully disintegrate up to two human-sized targets, and the disintegrate action can only be performed outside of combat (i.e. hiding the bodies). Note: In the TV Series, the disintegrate effect is only used in a small number of episodes in Season #1 and is relatively non-existent after that.
4) Replicator technology is immune to ZAT effects.
5) I agree with Valdore that the ZAT is a loud weapon with a very distinct and easily identifiable sound.