laminating a big piece like that is NOT a good Idea, it there is a scratsh or divit in wither sheet your $crued you will get a ugly bubble. but if lets say bolth peces are brand new and un marked then all you do is cover the one with a thin coat of Methylene chloride not acetone, acetone will work and well just not as well as Methylene chloride the you squish them together and your gold..., I would and did say do it go for it!!!, i think i was actuly one of the first to say it?, Even at 3/8 its a bit thin but like you said it profetionly done so its not like its going to leak, and the top trhe way it is its going to be plenty strong. Not like the rays are going to wreck it or anything.
Laminating will give to a stronger ank but for the trouble its forth i wouldnt, its worth the risk I think.