It turns out that my system using Mac OS X 10.9 doesn't much like old versions of iTunes - the ones with iTunes DJ - and as a result the means of updating Apple's stuff, the awful App Store, doesn't even work on third party software I want updated. Oh well, I'll replace some files and that'll be that.
It turns out that Nightingale plays my library in the way that iTunes used to before Apple's management downgraded it, although what's required is an add-on for it called Party Ruffle. Nightingale scoops up my iTunes library pretty handily and it works fine.
Goodbye iTunes.