The high variance does give you two tactical problems. First, how do you keep performance from getting worse? Typically you would set a threshold on the metrics, and prevent checking in code that breaks the threshold. With high variance you clearly cannot do this. Instead, make the barrier soft. If the performance tests break the threshold, then you need to get signoff from a manager or senior engineer. This way, you can continue to make coding progress while adding just enough friction that people are careful about making performance worse.
The second problem of high variance is showing that you're making progress. However, for you, this isn't a real problem. You're not talking about cutting 500 microseconds off a 16 millisecond frame render. You need to cut 5-25 second page loads down by a factor of 10 at least. There must be dozens of dead obvious problems taking up seconds of run time. Is Confluence's performance so atrocious that you couldn't statistically measure cutting the page load time in half?