> I think I can refresh a lightly dull blade in 10min or so, and speaking as a non-pro.
This is the same assumption (and problem) that every YouTube knife sharpening video makes.
The people who need those videos, by definition, have knives that are absurdly out of whack for some reason--super dull, badly sharpened by someone who "knew better", chipped because used like a cleaver, etc.
Those kinds of knives require a very coarse (150 grit or below) stone and quite a bit of time and attention on the first pass to fix. You will not fix it easily. You will not fix it in 10 minutes. You will not fix it with a 300 grit stone. You will not get any feedback from angle bite or a burr for a very long time. etc.
Most of the feedback mechanisms you rely on when sharpening with a whetstone do not exist when your knife is sufficiently out of whack. Learning to sharpen on a whetstone with such a knife is extremely difficult.
If you treated your knife like that, even a system wont help.
Either bring it to a professional with professional power tools or buy a new one and start being kind to your knives.
At the risk of triggering whetstone enthusiasts, once you have a properly ground knife, all you need is a two-sided 3000/8000 grit stone. I find that I can resharpen my semi-fancy knives within minutes to cleanly cut a sheet of paper. And I also finish with a leather strap.