I'm no expert but when I rout out a frame such as your's, I'll do a rough cut to remove most of the waste (red) and follow up with a flush trim bit and a guid made out of 4 pieces of scrap wood to use as a guide. Secure it with double sided tape and use a table top mounted router.

 

Yep, that pretty much covers it. And, if you want the corners square, instead of rounded, a bit of careful saw work will take care of that. Might want to practice with scrap first.

 

use your table saw to rough cut out the waste...
mark where the blade doesn't need to cut...
lower the blade all the way...
set the fence to how muck of border/frame you want...
set the panel up against the table saw fence and raise the blade all the way to max up through the panel...
make your cut..
turn the saw off and lower the blade...
turn the panel 90º and repeat the process...

don't forget that the saw blade is round and where you stop cutting on the top of the panel the blade will cut into the frame a bit further on the bottom side...
cut apiece of scrap and you'll see what I'm talking about and you use the test cut to gage/measure your cuts on the good piece...

 

"Is my thinking correct or is there an easier i. e. better way to do this?"
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Edge guide, whilst possible, is way too unwieldly if neatness counts.
I also would not plunge saw, an extremely dangerous practice.
What else? Cut most of the waste with a jig saw.
Then tack on some wide straight edges (back side) that map out the waste.
Now rout-flush-trim the waste. Guide bushing or bearings rolling along this
battery of straight edges.
Routers

 

Thinking farther down the road, what are you going to do with the waste left in the grooves of the rails and stiles where the existing panel fit in to?

What is the purpose of this mod? Your resulting frame will be pretty weak. Just sayin'

 

I did the silver frame of this box with the technic I mentioned above. It was made from a solid sheet of 3/4" MDF and notched a 1/4" underneath (think of the back side of a picture frame) to press fit around the box. The piece by itself would have very little strength but is strong when combined with the box. Also, had I built it like a typical frame, I'd worry I'd get failure at the corners over time.

One would assume the OP is wanting to do something very simular with the cabinet doors.

 

+1 on what Pat said.

Or, outside the box, why not cut 4 new strips out of the door, and make a new frame? Are the existing doors flat or fake panels?

 

Pat. beat me to it.

 

I simply take an oversized piece of scrap plywood or MDF and cut a template frame to the correct size on the table saw (as previously mentioned) and use a template guide bushing. The oversized frame will give you a steady rest for the router base. This can be used over again if you need to make multiple pieces the same size.

 

Thanks much for all the many replies and ideas. So more info on this. Okay I am not sure I can explain what this guy wants, (He is a programmer) He has a set of speakers, he wants to buy a cabinet and put the speakers inside the two cabinet doors and rout out the door as in the picture I posted.... but.... the door is from ikea and is made with Particleboard, Foil <http://www.ikea.com/us/en/catalog/products/90178466/>

So not sure if I will cut it as I think it would look rather bad and he would not be happy.

 

Regardless of how it will look, I can't believe the speakers will sound as good as I'm sure he expects if they are placed haphazardly in cabinet doors with no attention to the tuning of the enclosure. Properly matching speakers to a box involves a sealed enclosure, air tight, of a volume that compliments the Theil-Small parameters of the drivers (speakers). If not air tight then the box should be 'ported'. The port (a tube that extends into the box) needs to be the correct cross sectional area and length to be tuned to the remaining box volume after you subtract the volume of the port.

 

David
A lot of manufactures use mdf for speaker boxes, if you plan it right should work out well