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I have a bridge I would like to use, a belly bridge, EIR, but measures only .340" at its high point. All else being equal, is that enough wood?

Gibson acoustic bridges are about .25" thick so that dimension is not the issue. Your concern has to be for the saddle slot depth -- which in your case should be about .25" +/- most likely the saddle will need to be slightly taller so its important that it is well seated in the slot to prevent tippping toward the sound-hole. Tipping can also leverage on the front edge of the bridge and cause a crack.

Got it. Thanks.