I still consider Vanguards useless for gold runs as the adepts can do biotics better. If you use your Vanguard where you don't charge everywhere like you said it could be a useful class as you could use nova when you've been pushed back with enemies surrounding you. However I think there's better builds on offer depending on which enemy type you're facing but I'm willing to give this a go as it could work.
The Soilder is kind of all all-rounder class but it doesn't do anything great compared to specific builds tailored for what enemy type you're facing. If it's Geth you want energy drain + overload, if it's Reapers it's biotic explosions and for Cerberus you can have two snipers with cloak to do massive damage coupled with Adepts with Stasis.
We've did a few successful runs today against the Reapers centered around biotics. I put all my points into getting a really fast cooldown on warp while cruckeyee had points in his throw do do more damage with biotic explosions as well as no cool down for a successful biotic explosion. With 4 adepts I imagine you could just blitz through the Reapers.
I'll be on tonight but I reset all my high level characters but I've did Geth gold so much already that I'll be able to manage with a level 10.