(Roughly) when did medical science/major surgery begin to tip the survival rate in favour of saving more lives rather than causing deaths though bad practise?

I'm a medical statistician, not a historian, but it's an area I know a little about.

This is a really difficult question to answer because the records don't really exist to make an assessment of 'kills vs cures' and even the modern methods we use to demonstrate benefit (or otherwise) are neither perfect nor perfectly applied. The Atlantic published a well-referenced review of this problem recently which covers some, but by no means all, examples of poor practice: When Evidence Says No, but Doctors Say Yes. We are still killing people through lack of evidence or poor interpretation of the evidence: Medical research—still a scandal.

The balance is almost certainly positive nowadays but the largest advances in life expectancy have come through improvements in hygiene (especially access to clean water), reduced deaths in childbirth and lower child mortality. It's really quite difficult to quantify the benefits of a new treatment when we can do prospective trials on the topic; to do so through historical data is much harder, especially if you want to look at medicine as a whole rather than single defined topics.

Probably the closest you can get to an answer is the history of evidence-based medicine - the practice of checking whether theory translates into outcomes. As said, the applied science is still not done particularly well in all (perhaps most) cases and modern research structures provide many incentives to do it badly, but we can at least pinpoint some pivotal moments.

James Lind is widely credited with one of the first controlled trials, of treatments for scurvy in 1747:

Crucially, the Treatise contains a description of a very early ‘fair test’ – although the report of Lind’s controlled trial comparing six purported treatments for scurvy is rather hidden away and occupies just four pages, unmarked by a subheading, in the 450-page book. Lind reports the trial as having been undertaken in May 1747, while the Salisbury was at sea enforcing a blockade in the English Channel (Sutton 2004). Lind’s trial involved twelve sailors with scurvy, who were ‘as similar as I could have them,’ who were accommodated in the same quarters (the forehold), and had the same basic diet. His report thus illustrates his awareness of the need to guard against selection bias and shows how he tried to hold potential confounding factors constant – clinical condition, environment, and basic diet.

Just over a century later, Florence Nightingale pioneered the use of statistics in health care, in terms of pinpointing the causes of disease but also in persuading the authorities to invest in solutions.

The first randomised controlled trial is generally recognised to have been conducted by the MRC, streptomycin for tuberculosis, in 1948. Methods for observational studies, where prospective experiments are not possible, were pioneered by Richard Doll and others, necessitated by the battle to prove that smoking was killing people.

The evidence-based health movement really got going in the 1970s and 1980s, with the Cochrane Collaboration being perhaps its best known standard bearer.

I hope that's a reasonably useful answer as to why there (probably) is no answer. It would be impossible to come up with a reliable estimate of harm vs benefit just for the last 50 years. There's a large and fascinating history which I've only just touched on here. The James Lind Library was founded to tell the story and may be a good place to start if you're interested in the history of modern medicine from the perspective of harm vs benefit.