So if you play this when you're ahead on life, and have any life sink like Hex Parasite or Wall of Blood, you just win? (And even if you don't have one of those, it becomes a 4-mana, 7-toughness Platinum Angel that the opponent will absolutely have to remove before they can make any progress?)

Well, unless they're gonna win on decking or poison; yeah.

4-mana for a complete lockdown does seem a it unfair.

My late-night creations are hit-or-miss. I didn't realize this was such a lockdown/win condition when I created it.
Possible fixes:
1) Up the mana cost.
2.) Have it become "Whenever a player loses life, each players' life total becomes equal to the lowest life total among players." Also a reversed clause for gaining life.
3.) Change it to "If a player would gain life, each player loses that much life instead." Remove the second clause.
Also, change to a mythic rare.