I do not see how could I overcome the shortcomings of the 15-25 feet of cheap power cables in my apartment walls . . . by spending on the last 3-6 feet.In that case, consider spending on the *first* 3-6 feet. (Seriously, the nature of AC power makes this conceptualization just as valid.)
Also, you might think about running a dedicated line from your breaker panel to your audio system—clear up your identified shortcomings and a whole lot more. If your panel is really that close (15-25 feet), then this should be very straightforward.
So are there really good power cables that are also flexible?Of course there are. Some of our collective favorite power cords over time have been extremely flexible. I still use several TG SLVR PCs and a couple Michael Wolfe PCs—both very flexible and easy to route (especially the latter). I don’t know most of the PCs recommended in the thread so far, but they seem like contenders.
Finally, I know you have a local dealer (good for you, and all the best to them!) ... but if you don’t find what you need, you could consider getting together with The Cable Company and their lending program. Both for their initial recommendations and for the opportunity to try before you buy.