How to explain this acid-catalysed acetal rearrangement mechanistically?
You have managed to draw the correct acyclic hydrolized compound with a decent mechanism. 

This is a problem that can be solved by numbering the carbon atoms. Number the carbon atoms sequentially along the chain, starting with the acetal carbon (which has to be the carbonyl group). Likewise number the unpacked acyclic molecule. Use what you get to figure out which of the three hydroxy groups are used to make the second acetal.



In general, numbering your atoms using common structural features as anchors can help unravel complicated mechanism problems.