Baryta will be used in more papers than branded Baryta and the ones with the Baryta name attached vary on Baryta content. In short, there is no standard. I have mentioned this before, the categories Fiber and Baryta are vague and could even dissolve in a the wider category Fine Art, Photography papers that also covers papers with barite in their coatings.
Tecco Baryte BT 270gsm
Tecco Baryte Ivory BTI 290gsm
Sihl 4804 Prof. Photo Barite 290 gsm
FujiFilm Museum Baryte 300gsm
HP Baryte Satin Art 290gsm
Harman Baryta High Gloss 320gsm
Pictorico GKG Pro B&W Baryta Gloss 330gsm
which is probably the Gekko Green you already have.
Likely candidates without a Baryta indication in the name:
Pictorico GKR Pro B&W Cotton Gloss 265 gsm
Breathing Color Vibrance Rag 310gsm
Of the Baryta called I guess it will be a minimal content in:
Gekko Green
HM Baryta FB
FujiFilm Museum Baryte
I see today that Innova recently added a Baryta to its range:
Innova IFA69 Baryta 310gsm
My supplier adds the description (barite paper) to the
Innova IFA09 White Gloss 300gsm
The specs sheet of the Innova IFA39 Fibaprint White says:
-High white digital baryta paper-
I didn't check the other specification sheets but I expect there will be more barite containing papers.
met vriendelijke groeten, Ernst
New: Spectral plots of +250 inkjet papers:
http://www.pigment-print.com/spectralplots/spectrumviz_1.htm