a common problem with additions like these are that the heat load calculated doesn't count that the walls and ceilings are exposed areas that allow for more heat transmission than regular walls and attic floors. if the unit is undersized then your temps and pressures will all be the same as a properly sized one. the deciding factor would be the t stat not satisfying in an appropriate amount of time. this sound like the problem here. the return should be evaluated to see if it is pulling the hot air out of the area, also, you stated that when the sun goes down and it finally starts to cool down then thet stat satisfies, this supports the under sized idea. the color of the roof makes a big contrbution to heating the area. try a lighter color roof, roof ventilation or cooling the roof with water. have a contractor come in and do another manual J calc. to dbl check. hope you solve this!