Wait... are you saying that Gathering Storm actually works for you?
I'm assuming it does. Since it's only 0.5 second reduction per basic attack, my assumption is that I'm not seeing a noticeable effect because the skill is recharging normally at the same time. Some testing would have to be done to determine whether it's actually working. The thing is, this is the first I've heard that it might not work. Also, I'm not quite sure how I would go about testing this, given that a lot of skills don't actually trigger a cooldown unless you're in battle.
Anyway, I figure I'll post my Mage build as it ended up upon reaching Skyhold. I didn't level up during the In Your Heart Shall Burn quest, so this is the build I ended up with pre-Skyhold.
Storm
---------
Chain Lighting +
Stormbringer
Gathering Storm
Energy Barrage +
Inferno
----------
Immolate +
Flashpoint
Clean Burn
Winter
---------
Winter's Grasp +
Mana Surge
Winter Stillness
I used this to do everything pre-Skyhold, including beating the Fereldan Frostback. For that, I was level 11, and my party (Cassandra, Varric, and Solas, all using builds from the OP) was level 10 (I'd just hit Level 11, so my party was still a little behind). Fight took about 10-15 minutes, and the only person to die was Varric, and that was right at the end, so I left him down and finished the fight. Catch? I'm playing on Normal. I'm pretty sure that people are going to say that invalidates my results, but I got too the Frostback, so the game wouldn't let me save, even near the middle of the area. I even found a Dragonling, killed it, then waited for my party to sheath their weapons, but the game said I was still under attack. If I had been able to save just before the fight, I would have run the fight again on Nightmare to see how the build went.
Also, I added both Winter Stillness and Mana Surge to the build. Winter Stillness is about the only source of Mana Regen, as the OP pointed out. It's not reliable, but it's better than nothing, and I had an extra point. As for Mana Surge, it turns out that it triggers when your Barrier expires, as well, not just when enemies destroy it. That means that after combat, you can have your support Mage cast Barrier on you, then let it expire to trigger this. This means that your first spell in any fight costs no mana, allowing you to open up with, say, two Energy Barrages on the toughest target. That's 1584% Weapon Damage to a single target.
Anyway, I do want to point out that I'm not trying to say the builds in the OP are bad; they're not. They just aren't for everyone. My build isn't pushing out massive amounts of damage, but the damage is reliable, and you have the ability to hit multiple targets with everything except Energy Barrage, which is just about single-target damage. I'm presenting it partly as an alternative, and partly to try to spark some discussion about the Mage class's skills and options pre-Skyhold. If I come across as rude, then I apologize, as that's not my intent.