I have a flat roof with short attic space throughout. I believe it’s called a mansard roof. Live in S Fl and it’s very hot and humid. House is 2000 sq ft and a square. On all 4 sides there are many soffit vents that continuously pump out hot air. On roof I have one or two passive vents. Here’s the problem. I recently installed a screened patio on one of side of the house with insulated roof panels. The heat coming out the soffits is trapped under the panels and is unbearable.

Seems like my options are: Close these soffits and open more in other sides of house Install electric roof fans Install more passive roof vents

Do soffit fans exist? Am I missing anything?

Thanks in advance