Would Tryn be better balanced - while still being viable - if his Ult worked like a Blood DK?

For those not familiar, Blood Death Knights are a Spec for Death Knights in WoW, and the Death Knight's tanking spec. Their specialty as a tank is being absurdly hard to kill (at the cost of their overall DPS unless facing constant large mobs of enemies to affect with their disease DoTs). The skill I'm talking about is a Passive that they can have - called Purgatory now, but it changes names frequently throughout different expansions as Blizzard balances the classes. What Purgatory does is whenever the Blood DK would die, instead their health starts to go negative as they take damage and the healers have to constantly heal them. If the healers manage to get the Blood DK's health back into the positive window within a short time, the DK lives. If they can't by the time Purgatory expires, then the DK dies. The ability has an internal cooldown of 2-3 minutes, depending on the expansion and current balancing.

I bring this up in relation to because of the way his Ult works. Currently is a get out jail free card on an extrmely short cooldown that basically makes him immortal in lane and near impossible to kill unless you have multiple hard CC's all focused on him (Snares, Roots, Stuns etc.). Combined with his mobility, damage and self-healing, there isn't a lot of counterplay or interaction with ; either he does something absolutely retarded and dies, or he doesn't and never dies - all while taking towers and getting kills all day. Your only choices when he Ults are stun and flee, or hope you can outrun him; unlikely because of his W and E. Very few Champions have the ability to actually stand in combat against - it usually takes a team to do so.

So what if his Ult were changed to work like a DK's Purgatory? Tryn still gets to live, but now he must heal himself into positive health before it expires, or he will die too. This opens up the possibility of actually standing and fighting Tryn, and does a lot to curb his chickenshit "Ult-n-Run" playstyle. It gives you the actual ability to counter his Ult beyond "Have hard CC" and "Run like a little girl".

It also makes Tryndamere decide - do he want raw damage but less ability to survive their Ult - or the ability to heal himself in-Ult and come out of it more often (without the assistance of allies)?

And its not like the change would be thematically inappropriate for Tryn either.