Sump Drainage Problem

I have a sump pump in my basement that drains out into a dry well. Drainage during heavy seasonal rains has become an increasing problem over the last few years. There have been 3 occasions over the past 2 years where the water has backed up out of my pit into the basement but the sump pump itself has not failed. I believe that my dry well becomes over saturated and is preventing the pump from evacuating the water fast enough.

Although I can route the water out into the lawn, I would prefer to continue to use the dry well. It works 99% of the time and my washer drains into the pit. My fear is that draining into the front yard will be unsightly.

Is there any way to install an overflow valve on the pipe outside so it only drains into the yard if the dry well is full? Should I be looking at installing a new dry well? Any ideas or advice would be appreciated.