Any digital circuit can be made reversible using components like the Fredkin and Toffoli gates.  This includes SHA-256.  As much fun as it would be, there is no fundamental need to develop a new algorithm for the Bitcoin PoW.  It would truly be interesting to engineer a reversible SHA-256 computing device and see how it compares in speed vs. energy consumption against the current generation of non-reversible ASICs.  In practice only the hottest portions of the circuit benefit from being made reversible.  A hybrid circuit of both reversible and non-reversible sections is likely to be the one that gives the best trade-off of speed and efficiency.