Just got a blackstar studio 20 last week, and it fuzzes rather nastily on both the clean channel and overdrive channel.

It happens on low E and F notes, but particularly badly on the 12th and 13th fret of the low E string.

It has a beautiful clean sound, as far as I can tell from my limited experience. It's a shame that these notes sound disproportionately loud, and fizzle, when otherwise the sound is great.

What can I do to alleviate this? Can I RMA it if modifications are too expensive, or if it can't be fixed safely by me?

If it's relevant, I'm playing a PRS Hollowbody II through it, neck pickup (57/08) with the tone knob rolled off to 6.
i used to have a ht 40 that did the same thing. i completely tore it down and re glued the entire chasis, made sure everything was tight...it helped a little but not enough. Ive seen others with this same issue on other forums. you could go over it and make sure everything is tight, speaker, chasis, support blocks, etc. i dont know where you purchased from but if that doesnt help and If you like the tone otherwise i would send it back and get the head and 1x12 cab if possible. those combos are known for excess noise.