There is a lot to respond to here (and I think you're looking for responses) so I am just gonna stick with what I think are the key points and be brief.
> If you have a prior state that is in part systematic, and part random, is the randomness per se free will?
Let's please replace random with uncertain. If _part_ of an entangled system is uncertain the _whole_ system is uncertain [1].
> Does that encapsulate the notion of free will?
free will [2]
the power of acting without the constraint of necessity or fate;
the ability to act at one's own discretion.
To me this subjectively means: Are my choices the result of something greater than the material sum of my parts? Yes.
> That is, I cannot make you change your choice, only you can.
Your free will attempts at influencing me to make a certain choice would seem to entangle my state with your's and perhaps change the probability I will make one choice over another.
> If an omniscient external individual cannot alter your behavior,
'omniscient external individual' is a quite an assumption here.
> Why should the non-omniscient individual seeking change be held responsible?
Free will is the _only_ way to hold the individual responsible.
> but I think at some point the notion of free will starts to lead to counterintuitive problems and/or becomes very poorly definable. At some level I suspect it implies not only autonomy but complete agency, which is suspect.
(I may be misunderstanding you here) Free will over a decision must ultimately collapse to a choice made. At that point it is determined reality and no amount of free will can undo it.
You either took the Red pill or the Blue pill. If the decision is never observed the choice was never made ergo it didn't happen, it is not real.
In the spirit of Spinoza [3] I actually find bestowing free will upon particles very intuitive. We then have free will because it is an attribute of our fundamental components. If particles have no free will and are pre-determined we have no free will and are pre-determined. If we have free will then particles must have free will.
Full disclosure, I am an armchair philosopher with an interest in the cross-section with physics.
[1] https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
[2] https://www.google.com/search?q=define%3A+free+will
[3] https://en.wikipedia.org/wiki/Ethics_(Spinoza)