Less glossy can always be accomplished by knocking back a gloss finish with fine steel wool, or synthetic pads, or rottenstone on a felt pad.
If you wanted a film finish like nitro or poly you could seal the wood first with bullseye seal coat.
GA doesn't really need a finish though. I have a GA fretboard on a warmoth neck and it is so dense and smooth it positively refuses to get grungy.
Unfortunately that mahogany back is going to need a protective finish. In which case an oil based varnish (like Tru-oil) is not a bad idea.
Also, do be aware that GA tends to darken a bit when exposed to UV/sunlight.