Poa can do well in shaded and moist areas. Top selling bullet point for it. Conversely - it is extremely sensitive to drought and heat. Very low tolerance
A good wetting agent can increase drought and heat resistance exponentially. I mfg a wetting agent and many of my new mexico and arizona customers love the product exclusively because they continue to grow their veggies and/or flower gardens well into summer when everyone else packs it in till fall.
You will find alot of case studies (Hawaii University has a great one) on how important Humates are to nutrient density (drought/heat resistance due to sap health). It is the number one driver of making Phosphate available - and we all know that *zero* nutrients get into a plant without hitching a ride on the boat called Phosphate (this is how Roundup Glyphosate works - it simply blocks phosphate absorption)
I would experiment using a bio friendly soap, with a humate (low aluminum), along with a sugar - spraying or fertigating that 3x per week. If youre desparate for the results, apply daily spreading out the dosing
EDIT: in case its not known, wetting agents increase penetration (deeper and wider)
Great example video (rest of video content not sanctioned lol )