Looks like I really was just short last time, because this time I managed to get it to say “Infinity”. And I didn’t need “duplicate last ingredient” this time, just Rosemary, Mint, many duplicated Wyvern’s Tear and Lavender Oil, and one Traveler’s Herbal Tea.
I think there are enough instances of Echo on the mint that this would take an absurdly long time to actually finish scoring. Best guess based on the estimated number of bottles of Wyvern’s Tear (more than 100, not sure how many more), there are likely at least a million activations of the first Rosemary: more than 100x echo on Rosemary and each mint means at least 100x100x100. Given that every activation triples the scoring, the actual score (ignoring floating-point limitations) should be at least 3^1000000 points. But getting there would take days of scoring, since there at most a few activations per second.