I've got some of Devan's experience. Reformed MECP and Rockford Institute grad here...worked for an independent shop for a few years.
Full plexi is tough to make look right. Plexiglas is optically transparent (unlike most glass) so it is really unforgiving at seams and overlapping points. A window would be your best bet. If you're really into taking the time, and cutting holes...mounting the subwoofers in the rear deck (don't know about 12" fitting) with grille cloth covering them would be a really trick way to go. Then you can show off the baskets with the lighting in the trunk. One of my personal favorites is suspending the box from the rear deck so you still have a larger flat load floor and can even use the ski pass thru/fold down seats depending on application.
A nice compromise is building a ported box
Ported Box Calculator and running the ports into the cabin of the car. This can give you a certain amount of 'cabin gain' and lower the distorting effects of the subwoofers pounding on the back of your rear deck mounted speakers.
I don't agree with pwnt by pat. Building your box as part of your car isn't what you really need, IMHO. Also your Kenwood subs (and most others) are probably designed to be in a box (model #?) as IB or infinite baffle speakers are generally designed for that use only.
Just my 2cents.
P.S. Try to isolate the neon tubes from the vibration as much as possible, especially if they have the ballast built in. I've had some pretty regular failures due to the cheap transformers in the assemblies giving up. Either way make sure you can get back to them.