In that particular game, I probably should have just 2-base all-inned or hit an early 3-base timing to try to kill him, and it would have been a good percentage play, but I didn't. I decided to stay patient and get up to a big army that I thought couldn't be stopped.
You'll notice that throughout the late game, there's just no way I can engage. Any time I'd try, I would get my units pulled into spores, my Zealots would die to spines or Locusts, my Templar would get targeted by Locusts and would get fungaled if I wasn't careful.
The only possible way I can think of how to beat this, is to get a Mothership. Yes, that's right, the Mothership is back in PvZ.
The idea here is to get up to about 8-10 Tempests so you can start pushing his spine/spore wall, ever so slowly. The Mothership should be positioned in the back to prevent it from getting snagged by a Viper, while also providing cloaking for your Templar.
As Overseers move forward, you should fill the rest of your supply with Carriers and target them down the best you can. The Templar exist primarily to feedback Vipers and Infestors, as well as to land Storms if they are forced to engage into you. The push is going to take a long time, and will probably require you to reset over and over, but this is probably what late-game PvZ is going to turn into in the next 6 months or so.
Of course, if you ever get into a bad spot where you are surrounded or something, you can always use the Mothership to recall back and reset your push.
I honestly don't see any other way to fight the deep late-game turtle Zerg style, other than hoping you can kill them before they get that far. And the only way you can pull this off is with the Mothership Cloaking your Templar, dramatically reducing the usefulness of Swarm Hosts and allowing your Templar to feedback Vipers.