hello Rising_God...I've had some success with pure minion builds, but you're right, they tend to end up going long. They are much more stressful and take a lot more micro-intensive play. You can get kills, but it has to be the right situation. As for killing giants...this is not what your minions are for. If you are oak, you should be putting your ward down and fighting them directly while your minions tear down the enemy citadel. (you should've gotten surge to help you with this...) The ward helps two-fold, it replenishes your spirits to go tear down the enemy citadel and it gives you armor to decrease the damage from the giants.
If you are erebus, the same is true...but instead of surge, it is mist. Keep summoning your minions and sending them to the citadel. They can either fight them there or lock your portals. They can also spend a lot of money upgrading the citadel and buying gadgets. If this occurs...then you should have the edge on purchases.
If you are sedna or occ ...there is no competitive minion build.
I have never once played the QoT, so I can't tell you anything about her.
