I was not aware that any version of Model H software support the single ball drop system that appeared on later games. It might have first appeared on their MINI Skee Ball lanes which use different software. But I first saw it on Lightning Board system.
To my experience, Model H games have always had the 9 (or 6 which I have NEVER Seen) ball cradle assembly. When the game is started, the computer energizes the solenoid for a set amount of time to allow all 9 balls (or whatever is in the cradle) to drop. The solenoid is then turned off. As you said, there is no single ball switch AFTER the ball drop. Only at the top of the alley to register "Played Balls" both scored and gutters. With the single ball solenoid, the coil is left on until 9 balls have been served to the player. In theory, this means the game can operate with only 1 ball and, the solenoid could be energized indefinitely if there were no balls in the alley.
The single ball system was horrible when introduced on Skee Ball Lightning and Skee Ball Too! It had been used by others that made copies of Skee Ball but didn't copy the unique ball cradle assembly. The players had grown to expect 9 balls dropped on coin drop. When it didn't happen, they complained. The shorter alley allowed for only about 11 balls max. After that, any additional balls would take off played balls as the game was serving them to the player (extra balls sat above the switch after game over). Thereby shorting the player of the opportunity to play all 9 balls that were served to them.
I suppose for home use, you can just install 9 balls, let them drop, and then the balls played switch will do the rest. Other brands of lanes work this way and if there are 10 balls in a lane, they are served 10 balls. They game over when the 9th ball hits the balls played switch. This may take a few seconds so, if thrown fast, the 10th ball may still add score.
Regardless, according to the schematic, there is a Balls REL (Released) switch input at P2 Pin 9 (Balls Played is pin 11). But this switch is used for the 50 Point score switch for the 100 point bonus pocket software.
I really thought I had schematics to Model E (I had seen them and worked with repairing the boards before, like 25+ years ago). But I looked and could not find them in my files.
RB