Those appear to be older (early to mid 1980's) Reinke machines.

Your life will improve markedly if you replace the tower boxes. Reinke back then used individual components for the motor contactor and thermal overload, and the thermal switch was prone to failure. Their contactors didn't last all that well either.

Your over-running tower is due to one of two things: 

1. Either you have a frozen or bypassed alignment limit switch, or

2. Your "rain timer" in the second from end tower isn't counting down and it allows the end tower to run away.

Nebraska Irrigation has parts for those old machines as well. You can get replacement boxes and alignment switches from them.

On a machine that old, if you wanted to keep the existing boxes but replace only the crucial components, I'd replace all the microswitches (both travel and alignment), all the contactors/thermals with an integrated unit. You can do that for a lot less than $450/tower.