there are people other than me out there who say it works
There are plenty of people who say all manner of things. This does not make any of them any more correct.
and also there are people far more qualified than I am who will say it works beyond placebo effect.
Define "qualified." There are plenty of people with a vested interest in saying it works, saying it works. Be that the ones making money, the ones who want to save face after wasting money on it, and the ones like yourself who seem to just desperately want to believe in something. It's not a great shock to expect that a "qualified" homeopath is going to tell you how great homeopathy is.
Now, let's say you can suspend your belief and temporarily go along with the idea that homeopathy works and works beyond the placebo effect.
For it to work it would have to involve some kind of principle or process hitherto unknown to the scientific community at large and/or at odds with what we know so far.
You've got the cart before the horse here. You're right that for it to work beyond placebo it would have to be some mechanism that we've not isolated yet, but how it works is a secondary concern to if it works. The claimed mechanism is not the showstopper from a scientific perspective (it just makes it extremely unlikely); the problem is that irrespective of how it might or might not work, it doesn't. Homeopathy does not stand up to double-blind trials beyond placebo. It's that simple.
Whether water has a memory, whether it's the work of Jesus, whether it's innate alien technology or whether it's hitherto undiscovered nanobots, none of this matters, because, fundamentally, it does not work. So investigating how it works is an exercise in futility.
If water has a memory surely given it's central role in life on earth the water cycle and the age of the planet. Then all water molecules in existence will already have bumped into all active homeopathic compounds so tap water will in effect be a homeopathic cure all and we should not waste our time and money on the commercial version.
Ah, but, you've not shaken it in a special way.