If you recall I suggested removing those existing braces and replacing them after thinning the whole top. You mentioned that they are glued with a strong glue, but it is easy to remove them. I would chisel or plane down close to the glue line, then route the glue off with the raised area of timber down to your desired top thickness.
To help with the replacement of the braces maybe a bit of background will help.
Cross braces in an instrument are normally fitted as structural support, and carved down so as to enhance top movement but not lose their supporting strength. In order to support the downward pressure on the top the cross braces should go all the way to the sides, and are glued to them. In order to give the top the ability to vibrate/flex the braces are thinned strategically at their the ends.
An important part of cross braces is the joint where the two arms cross, this has to be tight.
I have shown two of a few different styles of bracing I have used, the small top area means less braces are needed and they can be light. Both these styles produced great sounding instruments. I have since gone lighter on both styles.
The bracing subject is far more involved than can be covered here, and involves many other factors that must be considered.
Mark I would suggest, if I may, that you could do a great experiment by tapping the top close to your ear, hanging between thumb and finger, I would expect it to sound dead with not much ring to it. Redo the bracing as mentioned and as you carve them tap and listen, that response will change, should come livelier and more musical. Sorry to ramble on.
In both pictures you added a layer of material around the sound holes, can you enlighten us as to the reason? Cosmetic, structural or ? Thanks