As a test, I used an admin spawned human and used admin tools to deal 200 burn damage, then timed how long it took for them to die. These times aren't precise as I don't have a stopwatch and had to alt tab back and forth, but are generally accurate within 1-2s.
Test 1: 2:28. Subject started taking brain damage after 1:47. Died with 664 respiration damage and 75 brain damage
Test 2: 0:56. Subject started taking brain damage after 0:35. Died with 297 respsiration damage and 36 brain damage.
Test 3 0:18. Subject started taking brain damage after 0:08. Died with 139 respiration damage and 18 brain damage.
Test 4: 1:33. Byond bugged and didn't update the scanner so I don't know when brain damage started. Died with 818 respiration damage and 102 brain damage.
Test 5: 1:43. Subject started taking brain damage after 1:05. Died with 530 respiration damage and 60 brain damage.
I'd hazard a guess that in a real scenario the odds any of those test dummies could have been saved by medical, even if it was staffed by the best medical players in existence is practically zero, simply because none of them would likely have made it to medical before dying. Keep in mind, these numbers are withn me using admin tools to deal 200 burn damage. In a realistic scenario where someone is taking brute by an antag or atmos death blender, it's probably going to be a lot worse.
There definitely needs to be some adjustments made on the time til death, and there certainly needs to be a floor so patients can't just randomly die in 20 seconds.
Edit: For some practical advice to anyone playing medical.
At round start acquire a bucket.
Go to the mendvend. Vend a bottle of Epi, Sal-Glu, Atropine, and Salylic Acid. Then vend 1 pill of Mannitol and 1 pill of Salbumtol. Add 20 of each bottle to the bucket, then disolve both pills in it. Grab a syringe and fill it. Inject literally everyone who comes into medical in crit with that. If you're the CMO, use your hypo instead of a syringe, it's faster. Normal hypos won't take atropine sadly, and if you have to give it separately it kind of defeats the point of the hypo being faster.
Edit 2: Actually, forget all that. Just carry Atropine, it's all you need. They can't die unless they suffer cardiac arrest, and they can't suffer cardiac arrest if they have Atropine in them. Defib if their heart is already stopped. Once atropine is in them, treat as normal to get them out of critical. In fact, it should generally be safe to just inject 15u of atropine from a syringe and then dump them into cryo as long as their heart isn't already stopped.
Edit 3: Theoretically, you should be able to just add atropine to the cryomix and just cryo everyone. Will require testing.
Once that's done, your biggest issue will be your fellow doctors trying to drag your patients away and throw them into cryo. I would recommend murdering them with a hatchet.