Yeah, I'm thinking access because cells work funny. Look at cancer -- cancer is, basically, rapid cell growth. Just in the wrong spot, with corrupted cells.
So say you need to heal internal bleeding in one of the intestines. You have a spell that encourages cell growth -- but there's also skin, muscle, the other intestines, stomach, kidneys and liver in the same general area and you don't want that spell to hit the wrong thing. If you're not careful then, congrats, your intestines stopped bleeding! But the bit of your liver that had been perfectly healthy before now has a tumor.
There's a reason that the book says you need medical knowledge to use healing spells.
Alternately, sometimes treating a consequence means having to take things out -- bullets, shards of teeth and metal, etc., in which case you might need to enlarge the entry wound to take something out.
Hmm, how would you feel about having a Doctor's Bag of functional utility spells, rather than the more application-specific "Biomancy" trees you outlined.
So for example, instead of a Treat Poison spell, you have a three-spell process, each of which might require different preparations and circumstances. Step one would be a basic Diagnostic spell where you touch a person's aura and are able to perceive the infection, the damage, etc. I'd probably say that in the case of poison you can identify the agent with a high enough roll, but for other things you'd need to recognize it based on it's effects on the body and treat accordingly.
Step 2 would be a telekinetic spell, something that can manipulate substances in the body directly. Call this one thaumaturgy so it requires an appropriate sample of the body (blood, skin, bone, brain matter, etc). Given a few moments of quite time for treatment it could isolate the foreign substance and make it inert, postponing any degradation of symptoms; think of it as a medial version of that permeable barrier that Elaine made that filtered smoke but not air, something that wraps the target and prevents the poison from reacting to anything and causes damage. It would then take a more extended Step Three treatment to then telekinetically 'bleed' the contaminant from the body (without causing damage and maybe exsanguination). This same spell could be used for general trauma first aid, to set bones, to stop bleeding or even to extract shrapnel.
Other toolkit spells might be a euphoric sort of psychomancy spell that acts as a short burst anesthetic, with a more powerful application causing mid to long term sleep.
A generic Water Magic spell to speed up the natural healing processes of the body, for long term treatment. A more powerful application might be to actually shapeshift the damage away (including massive issue damage and even loss of limbs). Would require a mental connection so that the change is at least partially guided by the person being heal (failure to do so might run afoul of the Laws as well as more immediate and mutagenic side effects).
If you are establishing a healing magic framework, it could also be a fun if they have a more powerful and all-encompassing Healing Ritual, as sort of Get-Out-Of-Jail Free card for the table, but one that gets less powerful the more they use it. Let the players bank say, one shift each per game session, and if they get enough and they can get back to HQ they have the option to invoke their healing spirit in a sunrise ritual, using up their stored shifts to fix something catastrophic. But if they rely on it too often then the ritual is less and less powerful, until eventually they are no more powerful than an aspirin and a cup of coffee.