To my knowledge, all the possible algorithmic optimizations have been developed and implemented since 2010 or 2011. Once you have as minimal a SHA256 implementation as possible, combined with retaining parts of the state for further calculation (as you describe), you can't really make it much faster in terms of software.
I believe the only optimization efforts possible beyond this point will be better utilization of GPU drivers (or maybe custom GPU drivers?), as well as designing new hardware.
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To my knowledge, all the possible algorithmic optimizations have been developed and implemented since 2010 or 2011. Once you have as minimal a SHA256 implementation as possible, combined with retaining parts of the state for further calculation (as you describe), you can't really make it much faster in terms of software.
I believe the only optimization efforts possible beyond this point will be better utilization of GPU drivers (or maybe custom GPU drivers?), as well as designing new hardware.