Quick update:
OmegaXTC has hit Rank 10 Chocobo and in the process has revealed a few interesting bits of additional information.
Firstly, the Chocobo's summon duration at Level #10 does appear to be 15 minutes as-predicted.
Secondly, getting from Level #9 to Level #10 takes a LONG time.
Thirdly, the Rank #7 Healer Stance's +30% Healing Buff looks to be very high uptime (75% or higher) which makes it probably the best survivability buff you can get aside from the Rank #4 Cure.
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For a min/maxxed general-purpose hybrid build, I'm now leaning towards:
+ Rank #3 Defender, Rank #6 Attacker, Rank #7 Healer (55 SP total)
Only having one weaponskill available in Defender stance (an +enmity attack) should mean that you can switch your Chicken into that stance whenever you want to
force him to pull maximum hate on something. Healing Stance will prevent him from autoattacking or using any weaponskills, and will make him start curebombing you whenever you drop below ~75% HP (in Free Stance he waits until ~50% HP). Free Stance would be used for the majority of situations, letting the Chocobo autoattack and cycle his heals and other damaging abilities as needed.
A note about Healing Stance: I could see it being useful for a Non-Melee Damage Dealer - someone who doesn't need any extra damage output and instead wants maximum survivability, but as a Paladin I
REALLY don't like using it. Aside from the DPS loss, my Chocobo has far too much of a tendency to stand right beside me and get hit with cone attacks, which means he now has to heal himself as well as me. Whilst tanking things I find leaving the Chicken in Free Stance makes me last longer, even with the lowered Cure trigger threshold... and the additional DPS doesn't hurt either!
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Suggested Chocobo Progression:
+ Level 1 (1 SP) - Rank 1 Healer (HoT) [0 SP remaining]
+ Level 2 (2 SP) - Rank 1 Defender (Enmity WS) + Rank 1 Attacker (WS) [0 SP remaining]
+ Level 3 (3 SP) - Rank 2 Healer (MND Trait) [1 SP remaining]
+ Level 4 (4 SP) - Rank 3 Healer (HP Trait) + Rank 2 Attacker [STR Trait] [0 SP remaining]
+ Level 5 (5 SP) - Rank 4 Healer (Cure) [1 SP Remaining]
+ Level 6 (6 SP) - Rank 3 Attacker (+HP Trait) + Rank 4 Attacker (DoT WS) [0 SP remaining]
+ Level 7 (7 SP) - Rank 5 Healer (Acc Trait) + Rank 2 Defender (STR Trait) [0 SP remaining]
+ Level 8 (8 SP) - Rank 6 Healer (Crit Rate Trait) [2 SP remaining]
+ Level 9 (9 SP) - Rank 7 Healer (+Potency Buff) + Rank 3 Defender (HP Trait) [1 SP remaining]
+ Level 10 (10 SP) - Rank 5 Attacker (Acc Trait) + Rank 6 Attacker (Crit Trait) [0 SP remaining]
Since it appears to take a very LONG time to get from Level 9 to Level 10, you could swap the level 9 + 10 choices around depending on whether you want more Survivability or more DPS earlier.