The first question I would ask is, "how much of the gain is due to the glass itself?". If the glass accounts for 50 percent, easy to work with that. If 15 percent, not so much. If it is a short peak at noon then nothing before or after, that is another matter- how many hours does the glass see sunlight and from what angle? Yes, a lot goes into it.
Here is a short primer on glass coating location:
If you are dealing with Low-E coatings on the "in-between" surfaces of double glass (I know you are not but bear with me here), there are two location options: The inside-facing surface of the outer pane or the outside-facing surface of the inner pane.
(Glass manufacturers refer to these as the surface numbers 2 and 3 and frankly I always forget were surface 1 starts! Outside or inside? The inside I think but I am not sure.)
Anyway, if the coating is on the inside face of the exterior pane, it is good for winter heating benefit to the interior because the air space allows reflection back into the space; radiant flux.
If on the outside surface of the interior pane it will better reflect solar radiation back out.
Both work for both situations, just that the right application works much better.
Now, I think you are referring to applied reflective films. The kind we always see as bronze and with bubbles and tears? If the film is installed on the outside of the glass, it will reflect more of the short wavelengths (UV mostly) but especially if a dark color, will absorb the longer wavelengths, namely infrared. The warmer surface will increase glass transmission gains by a factor of three or more because the glass surface, formerly about ambient is now 130 degrees or more. Ouch. Some of the IR radiation is blocked of course, does not penetrate the skin and re-emit on the inside but you about get it anyway.
So.... do you have a heat gain for the space especially broken down by surface type? That is where I would start. Sorry for rambling....
"If you do not know the answer, say, "I do not know the answer", and you will be right!"
-Ernie White, my Dad