From my
experience with septic systems your problem is not to much water added to the system, but blockage, probably from the tank to the leach field. The pipes collect a hard ring of material at every junction, like the junction to the leach field. When this ring narrows the goop can't flow to keep up and the system and over flows a small steady stream over the top of the leach field. To fix requires a pumping of the tank and cleaning the pipes of accumulated gunk from the house to the field. Many times this is done with a high pressure water snake. Then fill the tank part way with water to property jump start the system. I just had all of the done here at the current house I'm in, the flow on the surface killed a pine tree but made a blackberry bush huge and happy! We had to hack our way to find the tank again.
The best thing you can do for a stressed system is to not flush any non-biodegradable product i.e. toilet paper. Simply have a small flip top trash can in the bathrooms and instruct everyone to put their paper in it instead. This can be burned or composted. Do not limit water, I had friends in a area with limited water that removed just their laundry water from their system and had to go from pumping every three years to pumping every year, same amount of non-organic material but less water. Septic systems need water, cleaning on a regular basis and limited man made materials.
I wouldn't deal with the surface flow except to get it to stop, because eventually a partially clogged system with back up all the way to the house.
I hope this helps.