I have a few gallery prints that may or may not find their way into my physical portfolio. Whether or not I include them is influenced by the client.
I also use the same portfolio solution that you do for tear sheets, other samples, and printed work.
I show my commercial portfolio but have giclee and glossy fine prints on flapped boards separate. I show them in person if the circumstances (and viewing conditions) permit. (See comment regarding viewing conditions in the original post.)
It's important to keep in mind that any surface, other than a high gloss, has minuscule highlights on the ridges and peaks of the print surface that trashes the compressed shadow values.
Sprays, and finishes that attempt to diminish specular reflections do you no favour. Better to use oblique illumination rather than diffusion to diminish reflections to ensure greatest contrast range.
You may choose to change the (contrast) gamma of the print to enhance shadow detail to show what you wish under sub-standard conditions.
My mentors used to harp on "conform to practice." In other words, if you know how (location, lighting, position, size, etc.) the print is going to be used then prepare it to look its best under those conditions.
It's wasted effort to prepare some product that will not be used optimally by its intended user.