As a preface, we already knew that White Mage had the higest personal numbers of all the healers. this isn't a sudden revelation. No one is/should/will argue that point.
However, and firstly, This is not how DPS tests are calculated. Secondly, on this matter, you're comparing the application of TWO DoT effects Vs ONE. Not to mention, this is a singular application, and not done over several minutes. this makes things inherently flawed and biased.
Thirdly, you discount, heavily, the power of The Balance. The balance isn't a PERSONAL damage increase, but a TARGETED RAID damage increase. Balance on yourself is wasted. but that's ok, we'll give you a low-ball estimated stand-in using your own methods.
Let's use my as a Red Mage as a rough estimate for the other DPS. Don;t worry, it's ok, Since balance is targetted, my ilvl doesn't actually matter here.
My Verslows do ~ 5-7k, meaning roughly 10-14k per GCD, let's give this a spread balance of 10% and multiply it by 2 for the second DPS slot (lets be generous and go for a 4-man)
AST still has their 9k, but the DPS have shot up by 2-4k, and this is discounting the tank completely. AST is supplying an additional 5k for simply pulling a card. simply for existing. that's Per GCD for 30 seconds. if we're generous and say the tank does ~4k a swing, we can slap on even more damage.
Using your numbers, your WHM is bringing 10k actively, while AST is giving 5k by standing around doing absolutely nothing, and 13-14k doing their thing. you begin to see the power of a simple spread balance? this is a 4-man scenario, this get's blown much more out of proportion in 8-mans.
Small addition as I reloaded to see any additions: "100% random", in the grand scheme of things, isn't actually a major factor. Not only did AST get a great many tools to draw more and mitigate the RNG, but a SINGLE DRAWN balance is already enough value for a single pull attempt. Let us not forget that cards can be drawn pre-pull as well.
We account for 1 balance drawn because of this RNG. if we assume constant(100% uptime of) balance, then AST would, frankly, invalidate BOTH healers in every regard.