Glee Club is a long-standing feature of LibDem (and previously Liberal) Party Conferences: late on the final evening people gather and sing for a good few hours, aided by the regularly-updated Liberator Songbook, and possibly also by alcohol. I'd group the songs sung into three rough categories:
- Contemporary political songs from assorted points in history, sung pretty much straight (e.g. The Land, We Shall Overcome)
- Filks on well-known songs which comment on specific political events/arguments/personalities - there's usually at least one or two new ones of these each year, and the best keep on being included each year (e.g. The Lib/Lab Lie, Letterboxes, 12 Days of Merger/Coalition)
- Songs sung for the sheer joy of them (e.g. the various regional songs, anything performed by Pauline P)
Cabinet Battle #1 is explicitly political, though for Glee Club you'd need a confident performer to lead each section, and I think you'd have stop it at "I'll show you where the shoe fits" for it to work as a one-off.
The Room Where It Happens is all about power and who takes decisions and how (there's a whole lot of resonances for coalition e.g. "no one really knows how the parties get to yes / the pieces that are sacrificed in every game of chess"); for Glee Club I'd start it at "Two Virginians and an immigrant walk into a room" and cut the opening dialogue between Burr and Hamilton.
The Story of Tonight is a very feel-good little song about friendship and common cause, though not explicitly political
Hurricane in isolation is beautiful, and has a certain appeal to anyone who's written leaflet after leaflet attempting to persuade the public to vote for them.
You'll notice I've included nothing in category-2 - I think Hamilton is novel and excitingly political all by itself; maybe when it's old hat I'll be ready to think about filking some of it for political commentary, but that isn't this year. Also, I really love My Shot but it's really a bit long and complicated for a group mostly new to it; I think Wait For It is beautiful but the central attitude of "I'd rather wait for things to be explained/improved than do anything active about it" doesn't feel very LibDem.
If I had to pick just one, then I'd pick The Room Where It Happens. Though I confess I'd love to hear Pauline singing Burn.
 September is too far away for me to predict my state of recovery, but not so far away that I can handwave it as "surely I'll be done by then", as I have for e.g. Helsinki 2017. Also, politics really is off my priority list while I focus on a) recovery b) family c) work d) study so it's hard to justify the time/expense of Conference even when I am recovered.
 Yes, that's still pretty-much daily, yes it's been nearly three months, when normally I get over this repeat-listening phase in a week or two
 When I helped my mother move house a few years ago, I unpacked her collection of Songbooks, and spent a happy hour or two reading through them. I estimate it as at least 2/3 complete and has a lot of low numbers. The selection of what songs are included each year is its own little commentary on the political context. One day I want to write that up (or to read someone else doing so ...)