The solvent for acrylic is methylene chloride and is available at cheap-chemicals.com. You would have to flood the surface in order to get an invisible glue joint, but by the time you get the solvent on, you may have already passed out from the fumes. Good ventilation and a respirator would be essential. Perhaps you could rivet the thin pieces together, it may offer an interesting design challenge. Drilling into acrylic can be disastrous with a regular twist drill. Tap Plastics sells some that are specially ground for this purpose.