The scope and ambition of this dark musical by Theo Jamieson and Adam Lenson are boundless. A jagged, time- and space-travelling drama about the emotional wreckage of a mutually destructive relationship, it begins with reports of a young astronaut who has gone awol in a shuttle.

Why has Daniel (Stuart Thompson, fabulous) disappeared with such limited fuel and what is the point of his kamikaze journey? A non-sequential backstory emerges featuring his relationship with Emily (Poppy Gilbert, just as good) to build a chopped-up picture of their relationship, rather like The Last Five Years. It shows glimpses of formative traumas and cruelties. Daniel, bullied as a child, seems unconsciously drawn to someone who inflicts similar emotional damage. Emily lives in a state of guilt and betrayal passed on by her parents (especially her philandering film-maker father, who co-opts his teenage daughter into his web of infidelity and deception).

Directed by Lenson, the scenes between Emily and Daniel are arresting in their visceral rawness. Thompson and Gilbert show great strength of performance, with songs that soar and blast through you. The production has a wonderful, epic strangeness in its combination of parts: the interstellar projections, the emotional intelligence of Jamieson’s book, the accomplishment of his music, which is Sondheim-like at times, grandly symphonic at others.

But there are imperfections. Narrative purpose and motivation seem disjointed even beyond the non-sequential structure. You want to see the full, tragic shape of this relationship, which feels unfinished, with too many gaps in between. The “stranded in space” metaphor is overstretched (Daniel’s surname, Defoe, is an unnecessary nod to the writer of Robinson Crusoe). The storytelling as a whole feels lopsided, beginning as Daniel’s drama but then becoming Emily’s. Alongside them are three narrators (Simbi Akande, Gina Beck and Rupert Young) who provide commentaries with too many digressive cutaway scenes. Smaller details just hang: we hear how Emily’s father put her in an X-rated film at the age of 13, and that Daniel watched it in his childhood, but neither acknowledge this.

Yet there are glimmers of brilliance here, from the music to the mental-health drama. Flyby has the promise of becoming a musical like Next to Normal or Dear Evan Hansen – it could just do some very artful reordering.

• At Southwark Playhouse Borough, London, until 16 May