Raised Panel alternative for kitchen cabinet doors - question

Hello. I've gotten some great advice in this group related to my current project of refacing my kitchen cabinets. I've started preparing for the job and and I'm at a little impass. I can't make raised panel inserts for the doors (my router isn't up to the task and I don't have the bits or the time to glue all the boards). I'm planning on using oak plywood for the inserts but I'm a little confused.
I've got some sample pieces of 1/4" oak plywood, finished on one side but it measures 3/16", not 1/4". If I router out a 1/4" slot in the rails and stiles, won't that be too much looseness for the panel?
Also, the 1/4" plywood seems awful flimsy. Do you think it's thick enough for the middle insert?
Are there any other ideas? Is there a little bit thicker panel than 1/4" or do I have to go all the way to 1/2"?
Another question...Would it be a better idea to use 1/2" oak plywood (Is there such a thing as 3/8") and rabbet out the back of the rails and stiles instead of cutting a groove? I suspect that I would simply glue the panel into the back of the door but I doubt the finished look would be as good as sliding it into a groove, right?
These sound like dumb questions but I'd rather get it figured out now instead of finding out a week after the project is completed.
Thanks in advance!
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*Most* 1/4" plywood is actually 7/32". You can get router bits that size. You can also use a table saw and, with a little testing, run your rails and stiles (the "frame" of the doors) through once and turn them end for end and run them thru again to widen the slot to the correct thickness. The so called 1/4" plywood will work Ok because the strength of the door will be in the "frame" not the panel. These doors have the 1/4" (7/32") panels. http://tinyurl.com/3dvhhj
Max
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Buy a smaller bit, the same width as your panels. Or, cut thin shims and place them in the slots behind the panels.

Absolutely, glass is often used and is thinner.

You can go 3/8' but it will be slightly thinner, rabbit the edges to fit the slot.
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