"Until now, I've relied on setting the bid strategy to "maximize clicks" and letting it do all the work. My question is: how much of a performance gain can I expect with good manual tuning?
There is an alternative that you’ve not mentioned yet that has worked really well for us. That’s Google’s automatic Target CPA (Cost Per Acquisition) bidding.
Instead of trying to micro-manage bids you give the problem to Google and tell them to get you as many conversions as they can for $x per conversion.
I was initially skeptical when Google introduced automated bidding some years ago. We ran man vs machine tests periodically in several different markets to see if Google’s automation could beat a skilled human manager. In the early years the human managers beat Google’s automated bidding. Later it was close to a tie on about half the campaigns. After that Google’s automated bidding beat our human management every time.
We’ve switched over to Target CPA bidding on almost all campaigns and only have a human manage the bids manually right in the beginning and if the performance drops below a pre-determined threshold.
Just a warning: this doesn’t mean you can neglect the campaign. You’ve still got to check for negative keywords, set up tests etc. All automated bidding is doing is freeing up your time for those more valuable activities.