Since you are familiar with Armour Etch, I would start there. Apply a drop of Armour Etch to a scrap of your acrylic sheet and see if it reacts. If it does, you have your answer; just mask off the acrylic, cut out your lettering and apply as you would on glass.
If it doesn't work, and you really need it to be etched, you could try other chemicals which act as acrylic solvents. Some modelling glues work on a "plastic welding" technique where the glue dissolves the acrylic plastic so that two previously separate pieces become one. I would also think that pvc plumbing glue which works on the same principle would work (though you might not like it's purple color).
If you just want the etched look then your safest bet would be frost spray paint. It has the advantage that if it doesn't turn out like you want, you can probably wipe it off while it is still wet and try again.