When H+ is replaced, what the solution left is all H+ ions and anionic ions. As H+ has higher specific conductivity, conductivity increases.
When H+ is replaced, what the solution left is all OH- ions and cationic ions. As OH- has higher specific conductivity, conductivity increases.
When both H+/OH- in the solution, as H+ and OH- have higher specific conductivity than any other ion, conductivity increases.
Then all these three expectations are against the experimental results, does the measuring instrument have something wrong?