Is there any way to align temporally two signals in spectrogram?
You can find a large number of  &quot;model-based echo suppression&quot; or &quot;adaptive acoustic echo cancellation&quot; (for the keywords). They often combine a sparsifying transformation (wavelets, time-frequency decompositions) and some form of fitting or adaptation of the model to the time and frequency localization where the echo dwells. Underlying hypotheszs are:

the model somehow looks like the echo,
the similarity will increase in the transformed domain,
this representation will help the morphing, or make is more efficient (faster, etc.)

For voice, you find a look of literature, overviews, etc. You may also look at neighboring domains: vibration-based non-destructive testing or monitoring, ultrasounds. I would mention seimic processing, where echoes are sometimes named multiples (waves bounding several times between layers). Here are two examples I have been involved in. A first one quite fast which uses 1-tap adaptive filters (hint: a complex filter), the second  more involved with optimization constraints. They use time-scale wavelets, but could be readily adapted to short-term Fourier transforms or multi-input/multi-output filter banks.

Adaptive multiple subtraction with wavelet-based complex unary Wiener filters, 2012  (preprint)
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal, 2014 (preprint)