The dps requirements for the SSS dummies are unrealistically high compared to the actual fight, especially for BLM's, who are extremely reliant on thundercloud to proc in order to make the initial cast of thunder worthwhile. I probably use thunder a bit more than is recommended, but when I had trouble beating the SSS dummies consistently I tried several runs of either casting no thunder, or casting thunder only during the opener where a filler is absolutely required in order to get your full mana ticks. My dps was higher than a run if I had no procs, but was never enough to push a clear on the dummy. If I even got one proc in the 3 minute window then it would at the very least break even with the minimal thunder runs.
You seem to be aware that the dps requirements are vastly different, yet still hold to the thought that if you don't meet the dps check handily you will fail in the fight to enrage, regardless of mechanics. Assuming a party comp of DRK, WAR, SCH, AST, BLM, BRD, NIN, DRG, the total dps required for a5s SSS dummies is around 9500. This is nearly 1.5 times what's actually required, and if you factor out party buffs the "personal" dps required is much much lower. There's another thing SSS doesn't account for, is party buffs like AST cards and NIN trick attack, though the way it's not accounted for isn't in the "not needed" category, it's in the "oops we forgot to factor that out" category. It's also possible, though unlikely, that in translation the statement of "potions and food are not accounted for in SSS" came from "the additional damage from potions and food was not subtracted from the hp of dummies in the SSS." I'm also willing to bet that the dummies also don't account for the gear you get from savage, but that doesn't mean you shouldn't wear it.
Edit: I actually just learned that my latency has skyrocketed since I had to move my computer farther away from my router; the ~.5s that normally exists between casts on fflogs parses turned to .7-.8s for me after the move. This might be a contributing factor to why I was having trouble consistently clearing the SSS dummies before. I also forgot to mention that while food and pots aren't considered in the requirements for SSS, gear gotten from previous floors is considered. So if you're like my group and got 0 caster drops, then you have 2 or 3 pieces by now (i think?) which puts you a bit behind the expected gear for a6 SSS and way behind on the a7 and a8 ones.