Distressing purchased wall art
Since it's a plastic surface mediums made for use with acrylic paints might be your answer.

There are varnishes and glazing mediums specifically made for acrylic painting.

Both mediums start out clear. By tinting the mediums you will have control over the hue and value of the covering layer.

The company Golden caries a line if varnish and glazing medium formulated for acrylic paints.

Example Polymer Varnish
http://www.goldenpaints.com/technicalinfo_polvar

Example Glazing Liquid
https://www.goldenpaints.com/technicalinfo_glazeliq

The varnish is removable. The glazing medium is not.

Whichever method you choose to pursue I would do a test coat in a small area before trying to cover the whole canvas.

Or combine this with Ji Ugug idea and apply the medium to the glass (or plexiglass) cover and you won't have to worry about harming your canvas at all.