Barbaros timing with Broodfighter and GST - Urnbearer

[Paddywhack]

I wanted to make sure I'm not cheesing this interaction. As Broodfigher and Regen are two different abilities, I'm guessing you choose which to activate first. They don't just add together correct? Is the below sequence correct?

Barbaros with Grave Spirits Touch and no damage.

Start of Activation (Barbaros stays within 4" of Urnbearer throughout)

1. Broodfighter procs and overheals heals for 1, triggering a 2" move and Urnbearer to get Shielded +1.
2. Barbaros ends the free move within range of Urnbearer's Pools of Blood, triggering another over Heal of 1, giving Urnbearer another Shielded +1.
3. Regen +2 procs from Upgrade, overhealing for 2 and giving Shielded +1 to Urnbearer.

Urnbearer ends with Shielded +3.

[Adran]

I can't see any reason why it doesn't go as you say. 

I think Brood fighter and Regen are simultaneous, which means you pick one to resolve first, then the other.