Ive had some experience w/carbon fiber bodywork. Best bet is this
Layer of Plexi ======
Layer of epoxy ~~~~~
Layer of Carbon -------
Layer of Epoxy ~~~~~
Layer of Plexi ======
If you just try sealing the edges with some type of adheasive, there will always look like theres a line around the edge where the liquid ends. For body work we use gallons of epoxy. About $100/gallon of the good really clear stuff. There are cheaper ones that are more amber/yellow color. I bet you can use the 20/30 minute clear stuff that you find in squeeze bottles at your LHS. Do not get the 5 minute stuff that comes in a double barrel tube. You may want to try to run some scotch brite over the surface of the plexi that touches the epoxy so it bites better. Epoxy doesnt like to bond to smooth or dirty surfaces so make sure the panell is super clean (soap + hot water)
To ensure no bubbles in your CF cloth while doing this, first "paint" the plexi with the epoxy, then lay the DRY cloth on top of that. Carefully "paint" the cloth and after that, slowly lower the other plexi piece on top of that so you dont trap any bubbles.