We are listening to Jeff Wayne’s Musical version of War Of The Worlds in the car while we drive to London and I just thought - wouldn’t it be amazing if some of Big Finish’s stories were musical like that 
What story would you like a musical version of?
Trial of a Timelord. The whole season. Might have to recast the Valeyard and Sabalom Glitz, but lets get together Colin Baker, Nicola Bryant, Bonnie Langford, Brian Blessed, Nabil Shaban…
Well, there is always Doctor Who and the Pirates · Main Range • Episode 43 · TARDIS Guide, and I believe there is singing, of a sort, in Oh No It Isn’t! · Bernice Summerfield S1 • Episode 1 · TARDIS Guide
Not quite up to the sweeping majesty of War of the Worlds, though 
Bang-Bang-A-Boom could have done with more Eurovision goodness.
Bang-Bang-a-Boom! · Main Range • Episode 39 · TARDIS Guide (along with the similarly daft Max Warp · The Eighth Doctor Adventures S2 • Episode 2 · TARDIS Guide ) definitely qualify for ‘guilty pleasures’ for me!
My sibling continually advocates for a musical version of Ghost Light (I think they tried writing it at one point).
I want to say Inferno, and maybe The Girl Who Died/The Woman Who Lived. If we’re being extra hypothetical, then I also want to include the EDAs Kursaal and Beltempest.
Also, just imagine Scherzo: The Musical
Charley going all Disney Princess on how she is eating her own face 
Heaven Sent. Capaldi being chased round an ancient Castle playing his guitar the entire time 
As a committed Ghost Light lover and casual musical enjoyer, I would be really interested to hear what your sibling has to say about that!
In terms of audio dramas; The Marian Conspiracy, Master, and Other Lives seem well-structured for such a thing.
The Marian Conspiracy would do well as a Gilbert-and-Sullivan-esque semi-opera, with lots of people singing over each other and generally not listening to one another (ignore that six and Evelyn already have a G&S musical episode shhhh). This one feels possibly the easiest to adapt, as the source material already covers the main conceptual introductions so newcomers and General Musical Enthusiasts aren’t as left out.
Master feels very theatrical on its own and would be very at-home on a stage, even without songs, but also. imagine the dramatic, emotional solos. It would be a bit difficult to fully understand if watched without the context of like. a lot of the show AND audios, which i feel might be detrimental to casual fans and/or people being introduced to Doctor Who for the first time, but i’m sure something could be adapted.
Other Lives is perfect for one of those “what if we took an early/mid 20th century comedy-of-errors style musical but played everything for drama” deconstructions. Also i want to see how people approach the practical effects for C’rizz. This is possibly the least ideal for newcomers, but for the pool of people who already know the story and background it would be fun.
i’ve thought about this a normal amount :3
+1 to Ghost Light, I saw Sylvester in a few stage performances in the 90s, not necessarily musicals (the Invisible Man was amazing though), I can feel his stage presence as 7 booming across to the audience just thinking about it.
YOURE SO RIGHT ABOUT ALL OF THIS i can absolutely see Master being in the vein of ALW, especially Phantom of the Opera (since its already in the style of a gothic horror). I’m going to be rotating this concept in my mind i can tell already.
Welcome to the forum!
Last night I imagined a musical version of The Chimes of Midnight and now I have to see it happen!! 