I don't understand much of your post (d/t hail, vinyl siding vs regular siding, ect.), but the part I do understand concerns whether vinyl siding will help keeping the room cooler. The answer is no. No siding can make up for the lack of wall insulation, and if your installer is telling you about the virtues of the fan-fold insulation board under siding, he is just blowing smoke. That material just adds an R rating of about 1. Its real value is helping smooth out a slightly irregular substrate for the vinyl.
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