Anyway, am I right in thinking that dating events .................. about 3000 years ago using current software is unlikely to be accurate?

Well, I would ask the question how accurate do you want it? First. How accurate is the location you are targeting? Etc. And How many planetoids, comets asteroids does it need to factor in? Jupiter & Saturn must be factors you can't ignore, and the moon is receeding at about 1 cm a year which can't be insignificant. Chaos theory would demand these things not be ignored entirely.

All in all I would say the whole thing should be an humungous formula, and an iterative one at that.

To summarise the answer to the question. "near enough to keep you guessing" - probably.