We measured the photosynthesis at cloudy day was not changed in C3 plant, soybean, but decreased in C4 plant under greenhouse light allowing plant growth and development. Photosynthesis is dependent to light activating the plant hormones. I really wonder plant hormones can be used instead of light.

Using over-head water sprinklers would be very handy under songs ..

Increased level of plant hormone cytokinin (CK) can significantly enhance the photosynthesis rates. However, it can be difficult to establish the efficient protocol of cytokinin supply through the exogenous treatment such as leaf spray (e.g. time of spray, dose, etc.) and synchronize the treatment with plant metabolism. I imagine you would need to test various levels of CK (e.g. Zeatin, Kinetin, or BAP) delivered to plant during the periods of low light intensity. You may also look for microbial biofertilizers that help build the population of beneficial microbes that inhabit plants and secrete high levels of easily available CKs.