Good idea, I like the natural synergy it has with Badass, but...
1. Medicine Addict is a silly name. How about "Medic" or something.
2. What's all this "Yeah +1 to +3 armour is bad, how about 7 armor when you're at 175%-199%" tomfoolery?
+2-3 armor from TaN, +2-6 armor from blue/red armor (with bulk or power), +0-3 armor from Cyborg
That makes about 8 armor. This is already enough to make you roughly invincible. If you get the extra TaN and always top up your HP, it goes up to 10.
Attacks that deal more than 1 damage average when you have 10 armor: Baron (12), Mancubus, Revenant, all 3 bosses.
Say it was 7 armor instead of 3 at almost-max HP. Now you have 14 armor and the only attacks that do more than 15 damage are rockets (21) and AoD's melee (17).
The other idea for what to do with ironman is the 0.9.9 beta-only master trait that was taken out before public release, Regenerator.
Regenerator
No health globes? No problem! Your skin mends itself after terrible injuries like it was only a scratch! With this trait, you will slowly regenerate to a maximum of 10% of your HP per level. But that's not all! Whenever you feel relatively safe, you will instantly top yourself up to 20% HP per level!
Has 2 levels. Is an advanced trait, requires ironman 2. Should you injure yourself after feeling relatively safe (dummy), it will not heal you again.