I do my 'free' plate tuning with the bridge off. What I was finding was that gluing the bridge on before tuning didn't seem to make all that much difference in the frequencies: it added about as much stiffness as it did mass. The patterns were probably different shapes: at the time I was not paying as much attention to that as I do now. It was sort of a pain in the neck to deal with the top when it already had the bridge on it, and I could not find any good way to temporarily stick a bridge onto the top that was as stiff as gluing it, and that did not have a significant risk of messing up the top when you removed it.
When the guitar is together I find that gluing on the bridge drops the 'main top' tap tone by about 1/2 semitone, usually. It drops another 1/2 semitone or so in the first month or so of playing, at least on my instruments. Thus I try to get the 'main top' and 'main back' tap tones to be about the same pitch when the box is first glued up. I'm still having a lot of trouble getting the backs to work right. Maybe if I stayed with one back brace pattern for a while.....
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