You can get a 2 move healer (i.e. Chariot) to Medic III easily if you have a GG. You don't even need any promotions - just add a GG to a green unit and presto, 20xp.
2xp - Combat 1 (+10% Str)
5xp - Medic 1 (+10% healing)
10xp - Medic 2 (+10% healing on adjacent tiles)
17xp(GG needed) - Medic 3. (+15% healing) Total: +10% Str, +25% healing, +10% healing on adjacent tiles
That gets you +25% healing on the same tile, +10% on adjacent tiles. But that healer can never get better than that, if it’s a mounted unit. So I wouldn't call it a Super Healer.
To get to Woodsman 3/Medic 3, you need to start with a Melee unit (annoyingly, recon units can't get Woodsman 3, per the Civilopedia). The only 2-move early-game option I can think of here is Impis (bonus - Shaka is Aggressive, so you start with Combat 1). Of course, you can always upgrade a Warrior healer to Musketeer later on.
2xp - Woodsman 1 (+20% forest/jungle defense)
5xp - Woodsman 2 (double move in forest, +30% forest/jungle defense)
10xp - Woodsman 3 (+15% healing, +50% forest/jungle attack)
17xp - Combat 1 (+10% Str)
26xp - Medic 1 (+10% healing) Total: +10% Str, +25% healing, +50% attack/defense on forest/jungle
So the Woodsman line gets you to 25% healing at 26xp instead of 17xp, but you don't need a GG to do it. And if you have a GG or anticipate having one, you can get to 26xp that way pretty easily, anyway. Getting from 10xp to 17xp with your non-Woodsman healer without a GG is pretty risky.
No matter which path you take, you don't get to the full +40% healing (Medic 3/Woodsman 3) until 50xp unless you have some shortcuts (Aggressive, Charismatic, Jaguar, Quecha, etc). Practically speaking, unless you want to burn 2 GGs on your super healer, you
need one of those shortcuts. Starting with one of Aggressive/Quecha/Charismatic gets you there at 37xp, instead of 50xp. Starting with a Jaguar (free W1, plus Combat 1 since Monty is Aggressive) gets you there at 26xp. Charismatic+Aggressive gets you there at 28xp. If you play Boudica of the Aztecs, you can build a Jaguar with no Barracks, add a GG, and get a super healer at 20XP!