I think this is the right approach, but just to exhaust other avenues using a second roll, here’s a few alternative approaches for a Deadly Critical:
1. On a critical hit, the attacking player makes a Str or Dex roll (players choice), with the DC being the targets Constitution score. If successful target falls to zero hit points.
2. On a critical hit, the target makes a Con save. The DC equals 10 or half damage, whichever is highest.
My first suggestion above puts the roll in the hands of the attacker, which feels more Conanesque, the second roll is for the defender.
Of the two I prefer number 1. Both of these options will likely result in a higher chance of a Deadly Critical. However overall I think Xoth’s suggestion won’t dominate the standard DnD attritional combat in the way my two suggestions will, but at the same time still remaining a possibility. The low base chance for Xoths suggestion is also already increased by certain class abilities, so on reflection it feels about right.