Troy ... you can make wider pieces to attach to the inside ... back ... of the stiles.
I do my false fronts the same way, matching the drawers to the doors. Don't like the long drawer front, looks fake, and people pay me a lot to design and build their kitchens. I glue and screw a piece of 3/8 BB on the back side and use drawer front adjusters to install.
I finally found a fantastic solution to the inset false sink front dilemma. A friend suggested running a piece of metal behind the opening and then embedding magnets in the false fronts. I used a piece of angle iron (screwed from inside the cabinet into the face frame on each side; it痴 rigid enough that it doesn稚 need connected to the center stile) and then used neodymium magnets in the drawer fronts. I got a pack of 10 magnets from Amazon for about $10. The solution worked great. The false fronts are removable if needed, but the magnets hold them solidly in place. They don稚 move at all on their own, but with a little pressure, I知 able to slide them in the opening to get the desired spacing. It was a super easy solution!
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'I知 building inset kitchen cabinets, and I hit a snag with the false/dummy (I知 not sure what they should be called) sink fronts. In hindsight, I知 realizing I should have made two larger doors or one long false drawer front, or at least installed it all before the sink and countertop were installed.'
It's not the worst thing you could do. Really, don't panic. Here are plenty of ideas how to fix it. ANyway, you've made a great work already and just don't give up.
I know you have your answer - but just a compliment - they look fantastic.