I believe natural gas plants have a minimum idle so they can respond to the volatility of energy demand that needs to be met in real time. I don't think you can run the plants at 0 during the entire day and start them up again quick to respond immensely at 6pm.

If only there was a pattern to calibrate gas usage to... like a particular time when the sun goes down :D

As long as there is gas in the mix in my opinion it is not a "too much solar" but a distribution and storage problem.