If the two pieces of acrylic are touching (at the near-molecular level), you should not have a problem. One thing you need to keep in mind, though, is the thicker you make the acrylic, the less light you can trap. I have a 3/8” sheet that works fine.
To test, get the seam between them wet and see if it works. If so, you should get some MC-Bond. It will dissolve the acrylic, and reform it as it dries. You can literally fuse the two sheets together as if they were one. It’s how professional acrylic houses fabricate things.
It will also allow you to clean the drill holes for your LEDs (so you have a seamless transition into the acrylic). It doesn’t dissolve epoxy though, so if you get epoxy-based LEDs, they will be removable.