I've been investigating a possible Restrained Sudoku formulation:

Cells a knights move apart must be nonconsecutive.

For each value placed it removes up to 16 extra candidates compared to plain sudoku.

I am not at present sure whether it has feasible solutions, but if it does the solution space will be small.

After a weekend of playing around with it manually this is the least unfeasible solution I've found: It contains 14 failures: five of 89, four of 78, three of 67 and two of 56.

I would welcome any thoughts on how to take this further.