Doctors have a similar problem: too much uncertainty which can't be eliminated until the treatment is completed. They can't even tell you how much an office visit costs, because of the variability in how much time each patient needs, involvement of nurses and PAs, and any tests that must be performed.
Lab tests are a little better: they tend to take a predictable amount of time to perform, and the analysis is pretty standardized, but there's probably still some variability when the results are not routine. That explains the fairly narrow range you were eventually able to get.
I think we've got the wrong pricing model in mind for healthcare. Instead of itemizing every little action, test, and pill, we should be aggregating these costs. Pay medical professionals fixed salaries, fund institutions using budgets for fixed costs and consumables costs, and pay for it all via taxation as a common good, like public education, libraries, defense, etc.