Well, I'll be darned. I must admit I approached your solution with misgivings for two reasons: 1) After my experiences with my two ATVs, I figured there was nothing to be done but to wait for the next update, and 2) I'm obviously getting more cynical in my old age... 😉
Anyway, I did as you described with my AirPort Extreme, and had the same results (I have about 14,000 photos). Thank you so much for finding this solution (and I agree with the point made at the end of your post!).
I guess it isn't still the optimal solution (after all, everything worked fine with the router I had before I got the Extreme, so I don't know what I'd do if I had the old router)--plus it means I can still whine about the update causing the problem in the first place. Nevertheless, the slideshow DOES work now; once again, thank you for your efforts. Cheers!