Closed shows have been represented. In 1979 Dorothy Loudon did a solo of "50 %" from the closed BALLROOM and in 1987 Judy Kuhn and Dick Latessa did the title song from RAGS. That said, I can't see theme gathering the entire casts of either RAGTIME or FINIAN'S...best we might get is a solo or duet or maybe a montage taken from the press rolls.
Why do you think "Glamourous Life" would be dull? Is it not well staged and choreographed in this production? I suppose a montage from NIGHT MUSIC would be best to get a bit of "Clowns" in there and end with the finale of "Weekend."
A medley from LA CAGE might be most effective too but not "WE Are what we Are/I Am What I Am" because that is what they did in 1984. I agree "Best of Times" is the show's best number, but maybe re-routine it so both stars get to take part. (Numbers have been re-routined for the awards before: Look at THE FULL MONTY on the 2001 Tonys. And look at teh completely new version of "Love Changes Everything" from ASPECTS OF LOVE in 1990.)
Consider this: The Tony Award telecast has 12 10 1/2-minute segments. Segment 1 -Opening number and first two awards
Segments 2 thru 11 have two or three awards plus a scene or number from a nominated play or musical. The final segment has the final award(s) and a closing number. I would hope they do the right thing and get the plays in there though I can only recall a few scenes excerpted from plays that ever really worked. (Top of the list is Maggie Smith and Margaret Tyzack from LETTUCE AND LOVAGE in 1990.)But the plays deserve more than just a few lines. They need a contextual scene.
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com