Keeping it clean during while fitting a "traditional" frame design is do-able. Just spray both sides of everything thoroughly with the Kintronics pneumatic ionizing gun. That actually removes all static charge, while the brushes and other methods only dissipate a portion of it. The gun requires 60-75 psi (ideal pressure range) compressed air & costs about $375 as I recall, but it's worth it.
No matter what, static charge will come back to sheet acrylic in a short time -- minutes or hours, depending on ambient conditions.
And when the static comes back, the art paper will be drawn to the acrylic. You didn't describe the art paper, but it would have to be pretty stiff to resist deflecting as far as necessary to achieve cling. Even if you retain the edges securely and use 3" spacers under the acrylic, I'd bet the center of the art paper would bellow out & cling to the acrylic. Murphy's Law prevails.
This may be a good candidate for the acrylic sandwich mount. That is, sandwich the art between two pieces of acrylic and then frame the package between two more pieces of acrylic, with the outer glazings spaced away from the mount, to provide an insulating air gap.
Yes, it's a controversial mount, but if I owned a piece of art like that (Lord, kill me now) I would rather have a small amount of the charcoal pressed on the face, instead of the cockled, deflected art paper and black dust all over everything.
Also, I believe the acrylic sandwich mount would be less invasive than any kind of adhesive mount.
I remember someone highly knowledgeable (Hugh Phibbs, as I recall) talking in class about some decades-old pastels that had been pressed against the glass of their frames, and showed surprisingly little damage.