Fascinatingly, at a previous ecommerce gig, we had a similar issue. On of the developers ran a test where on one of our main pages, he added performance improve

Fascinatingly, at a previous ecommerce gig, we had a similar issue. On of the developers ran a test where on one of our main pages, he added performance improvements to get the fastest speed to a reasonable place, and then segmented traffic into buckets that deliberately slowed the server response by various, increasing amounts of time. And wouldn't you know, it made almost no difference on our primary conversion metrics. As far as we could tell his methodology was sound, but unfortunately it got buried when it was discovered the findings could be abused to show that performance doesn't matter.