Bitter experience has taught me that clients are no less demanding and full of expectations if you are doing something for free
Ain't that the truth! – not that I have much experience working for free or anything. Most of the work I have done without compensation is for direct family members. That is a much different situation than dealing with someone you don't know. If my mom or dad needs some help with something I'll normally do it but it is not a priority.
The same situation where I might not want to do something for even a friend I will just say I can't do it, don't have time, outside my expertise or some other line to get off the hook without sounding like a dbag. I haven't been in the situation of doing free work for a complete stranger though. It has always been friends and family as a favor/nice gesture.
It would be hard to speculate how I would handle a stranger just for the fact I have no desire or need to whore myself away to a complete stranger. If I were in that position though I would probably just tell them it is my way or the high way. If you are so desperate that you need to do free work to pad a portfolio or whatever than you have probably already lost the battle. People will easily take advantage of that to. I mean that is what smart people do take advantage of others.
So at a point I would think regardless of how much you want the experience/portfolio piece dump the work and move on. Send a direct message to the person that they need you more than you need them. That might be the only thing that registers with them.
Again though much of the best way to approach it lies in the relationship with the individual for whom the work is being done. It probably wouldn't be in your best interest to tell a friend or friend-of a friend to go f**k off but a complete stranger – perhaps.