try calling a plastic supplier and ask them what they would use since they come across these problems more often then we would. Let us know b/c I'm gonna work with acrylic in the future.
Alcohol Gel,(isopropyl alcohol)like the stuff you get in little plastic squeeze bottles to clean your hands works great.Just rub some on to the dry glue,wait a minute and rub it of with the end of a handkerchief or cloth napkin.
And, BTW, never use acetone (acrylic solvent) or paint thinner(MEK) to remove dried backing paper glue.All these will permanently and immediately eat into the acrylic and cause a permanent scar which will be very difficult to remove except by sanding and buffing.
Hopefully you have not trashed it yet...you should use a product made by PPG called "Acryli-Clean" DX330 - it is specifically designed for automotive acrylic finishes. I often use it to remove sticky labels...it works wonders.
I would still test it, but this stuff should do the job - I believe any decent paint store should carry it...I'd guess less than $10 will cover it.