Thanks for letting us know. That sounds like an exceptional case from our metrics. Would you be willing to share your Asana user ID so we could learn more?
Using store state vs local state shouldn't matter much, as long as your components are pure and only pull what they need from the store.
Sometimes but not always, reloading the page fixes the problem; it does seem to be more likely to happen when the page has been open for an extended period, but sometimes the problem persists after a fresh page load. (There's one project that I use to organize most of my work, and I'm liable to leave that tab open to that project without reloading or even changing the sort/filter for weeks on end.)
"Tracer bullets". Have a flag that can be put on an action that causes it to be logged very verbosely. In a way that travels through your system. And then aggregate those logs, process them, and make them available. Then randomly tag a small fraction of actions with that flag. Like 0.1%. Because you do this relatively rarely, you can make verbose logs without overwhelming your system.
When you receive a complaint about foo occasionally being slow your first stop is to see if you've got a concrete action that was slow, look at the picture from the logs, and try to figure out why. This will greatly help in reproducing rare problems or, if you can't, at least identifying where they come from deep in your system.