"Flat top" guitars usually aren't: they have a small arch built into the top. The amount of arch changes somewhat with ambient humidity. The measurements you have provided are within a typical amount of arch for the top and doesn't constitute "bellying". Bellying is, generally, a more localized distortion of the top caused by string pull.
One of the largest structural elements on the guitar top is the bridge. When the bridge is no longer adhered to the top, it isn't providing much structural support.
Most guitars with "decorative" dots on the bridge conceal bolts. The dots can often be removed undamaged and reused. A very small chisel works to pry an edge, as can any small, sharp instrument. Once the dots are removed, clean-out any dried glue concealing the head of the bolt. Removing the bolt should be fairly easy with an appropriate screw driver and a pair of pliers on the inside to grab the nut.
From there, removal of the bridge should be easy with a wide chisel or thin bladed paint/drywall spatula. Once removed, you'll need to remove all old glue and any finish under the footprint of the bridge. You can use 3/16" nuts and bolts through two bridge pin holes, and appropriate gluing cauls, inside and out, to clamp the bridge while the glue dries.
You won't likely want or need Bridge Doctors and the like. If you feel one is needed, you can always add it after the fact.
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