First, getting the Greenfield wheel-drive tensioning pulley to click into the next adjustment point: this is often an issue, and owners need to get used to applying a small crowbar to the pulley linkage when necessary to get it to click. This is more comfortable and dignified than using your foot.
Second, most hour meters are 12 Volt, and they run whenever 12 Volts is applied to them. Since you are trying to increase the hours not decrease them, I guess I'm not compounding a misdemeanor when I suggest all you need to do is connect the new hour meter to a 12 Volt battery for the appropriate number of hours. However I think most people expect the meter to reflect the number of hours the mower has run, not the engine.