I am new to Resolume but here are my ideas:
1. Import the audio file into Resolume and create your visual show in advance
You could include audio cues (perhaps a tone generator/peak) in the recording to quickly find the scene changes desired. Or even break up your audio clips into pieces and map to visuals, so they play together once done.
2. If YOUR timing is perfect, pre-plan the clip changes in advance
3. Press play on your recording, and manually record your visuals in advance.
You mentioned manually triggering is out - but OSC or small MIDI controller (even a foot pedal) could be used if you change your mind.
Let me know how you work it out!