Each idea is it's own and is not to be combined with each other.

1. Heal 25 HP when claiming an offering.
Pros: The main objective becomes more appealing.
Cons: Players may ignore their teammates in need to take an offering for HP; also, once you have all objectives, there's no way to heal.

2. Add a health boost somewhere in the middle.
Pros: Anyone can claim it.
Cons: Players fighting over the boost may ignore objectives.

3. Add a health boost to each team, somewhere away from their base.
Pros: Each team has a heal.
Cons: Teammates may fight over it.

4. Add a neutral shrine in the middle, that when captured, heals the entire team for 10 HP every 15 seconds. Can remove your own offering. Shrine does not count for the 3 so it must be used with care.
Pros: Everyone can heal.
Cons: May be a bit strong when combined with Guardian's blessing.

5. Add a neutral shrine in a randomized location (near the center line), that when captured [...]
Pros: Random location means you have to locate it first, wasting time that could be used to steal an offering.
Cons: May be a bit strong when combined with Guardian's blessing.

6. Add a fake offering hidden in the map that cannot be seen on radar. When picked up, heal 30 HP. Respawns in random locations every two minutes.
Pros: Spawn is random, so no player can find it on experience.
Cons: May be a problem if it continuously spawns near one team and not the other.

7. Add a fake offering hidden in the map that cannot be seen on radar. When claimed in a shrine, it disappears and instead heals 30 HP. Respawns in random locations every two minutes.
Pros: Adds a layer of surprise if you get it.
Cons: May upset the player if they wanted an actual offering and not a heal.

8. Add an invisible object that can be activated, and it heals 30 HP. Randomly spawns every two minutes.
Pros: Since it's invisible, there's no way to see where it is.
Cons: Players that need HP have no way of knowing where it is.

9. When all shrines are placed, heal 25 HP.
Pros: Gives winning team HP for the upcoming battle.
Cons: May be unfair to losing team.

10. Do nothing.
Pros: Heroes with healing feats have an advantage.
Cons: Heroes without healing feats are at a disadvantage.