So I wouldn't remove doomed with the various heals, that I think takes away the entire purpose of the condition....you are going to die, there is nothing to be done.
However, to me the plot power of doomed is it doesn't kill you until the "proper time". So in this example, the hill giant crushes you. The clerics heals you up, but whispers in your ear that part of the damage was so severe that he couldn't heal it....and in time you are going to die.
Now the DM and the player can work through that timing. Maybe its the end of the adventure, or waits until the end of the arc. What's fun is plotwise the character KNOWS they are going to die, so maybe they become reckless, maybe they become more sentimental, maybe they try to throw themselves at danger to take a hit for other party members. It becomes a significant part of the roleplaying, and allows for a truly memorable "end" to that character.
I think the issue most people have is not death but "lame death", doomed gives you the chance to have a death that matters. So yeah I like that concept a lot.
Oh, well... yeah. But I just mean that's the RAW for Doomed.
"A doomed creature has sustained damage to their
body, mind, and spirit that puts it beyond the help
of normal recovery and lesser magic. While the
symptoms of a doomed creature’s injuries might be
removed, only powerful spells such as regeneration
or resurrection can spare it from death or restore it
to life.
Suffering the effects of 5 or more levels of fatigue is
one way to become doomed; however at the Narrator’s
discretion a creature might become doomed
for any number of other reasons."
I figure spells like Regeneration, Heal, Revivify... those would work on the Doomed Condition.
But... I also -love- your idea, here, Stalker. That a person who is Doomed can still matter in the battle for a last desperate stand by still getting hit points but not really "Healed" in a true sense...
Maybe Healing done to a Doomed creature can become Temp HP lost at the end of the scene? That could be a good solid way to handle things, I think.