Too many Stamina abilities on bar one, that's why you are having troubles sustaining while using it.
I'd drop Soul Trap - It's not very good outside of filling soulstones.
I'd drop Silver Bolts - It's not that good outside of Daedra/Undead and as a Stamina Dump for pure casters. You can sub this back in for one of your 2H attacks if you end up needing it.
I'd also drop one of the 3 2H attacks.
If you dropped the charge you could replace it with the Magicka Templar Charge if you feel you need a charge. Otherwise you could add in Biting Jabs or Reflective Light. Solar Barrage might not be a bad idea also. Perhaps even swap another 2H ability for Cleave (morphed to Brawler).
You now have a nice AoE bar, Solar Barrage works great with Reflective Light and Brawler but won't give its bonus to Puncturing Strikes.
Then I'd take another look at bar 2, you're resto staff but not using any resto staff abilities - which isn't necessarily bad since resto staff does bring other stuff to the table (+10% damage while at full health and 10% Magicka return on completing a heavy attack). It also allows you to level up the skill for later levels. But if you're not needing any of those things maybe look at running something else - Bow would be good here.
If you stay resto I would put regeneration on your bar and maybe try to move Honor the Dead to Bar 1 so you have a healing option there (if there is room). You don't have a ton of great single target options in Templar (especially if you morphed to Solar Barrage and Reflective Light) which is why I probably wouldn't use Resto Staff in this setup.
If you go Bow then Venom Arrow and Magnum Shot would make great additions to bar 2, maybe even Bombard. You could also run Restoring Aura to help with Stamina Regen and Piercing Javelin would be a fine sub for Magnum Shot if you find yourself not having enough Stamina to go around.
If you're open to other ideas DW might work well instead of 2H, a combination of Blood Craze, Degeneration and Force Siphon can provide a really nice amount of sustain on single targets and Solar Barrage/BitingJabs/Whirlwind/CrescentSweep is a ton of AoE - always try to follow up Solar Barrage with Crescent Sweep because it has a much higher Damage coefficient than your other skills.
Sorry if I you feel I took your build idea and threw it out (kinda suggesting to go dw/bow over 2h/resto) as that wasn't my intention at all just kinda putting some ideas out there.