For example, you could take half the previous spectrogram, shift it to the left, and then use the inpainting algorithm to make the next bit... Do that repeatedly, while smoothly adjusting the prompt, and I think you'd get pretty good results.
And you could improve on this even more by having a non-linear time scale in the spectrograms. Have 75% of the image be linear, but the remaining 25% represent an exponentially downsampled version of history. That way, the model has access to what was happening seconds, minutes, and hours ago (although less detail for longer time periods ago).