Was this discovery made as soon as was theoretically possible, or are we rationalizing reasons to justify why it was in fact fairly slow? Or to put it another way, it seems like it was fairly slow, could we do better if the process of Science was different?

Like for instance, balancing the cost of putting researchers on the case, trying different combinations of antibiotics (which as experiments go shouldn't be too much of a health risk, neither too much of a material cost) on people with peptic ulcer, against the bayesian evidence for and against the bacterial hypothesis?

Even if the evidence was low, the cost to implement such a research project probably is lower than what's invested in bogus medicine like homeopathics or the like, which has more evidence against itself (at least a bacteria is more likely a causal phenomenon for something than magical water memory).