No definitive answer really. Bench, or replace the guts, or arrange a new mounting setup.
Most likely you'd replace the guts of the existing PSU. You could either cut the opening larger and run a ATX lead from a small PSU inside the original PSU housing. Or you could make a 5x2 extension lead. Or you could use the original connector, desolder it and solder it's wires to this board, so that it mounts exactly as before, and you plug the ATX to the PSU end.
It depends what suits you best. I've not built one into something yet. Likely I will in the next few weeks, but I need to research what PSUs I want to use in my setup.