What I have done is. First get a wooden ruler and lay it across the top in two or three directions, take photos which show the gap under the ruler. Next fit the new strings and (in this case) tune up to say eACF and repeat with the photos. Compare the photos and see if the gap under the ruler has started to change, this is an indication of how the top is responding to the stress. If you are seeing something you don't like stop right there. If you are happy, tune up the gCEA and repeat. After you tune the uke up don't let the uke out of sight and repeat after 1800 seconds (30 minutes). If you are really keen you can measure the gap, but usually comparing the photos is enough.
After doing this with several instruments I don't bother anymore. I have never been happy with the way the top looks when I tune a bari up to C tuning. Anyway I have a concert that has C tuning. I just buy the strings that are sold in local shops which are either classical guitar sets or daddario baritone strings and put them on. Tune to g tuning and play the thing. I have worked on my technique so I can make the uke sound soft, loud, dull, resonant etc by the way I play. On your fretting hand you can strangle the neck or fret with feather softness, on the strumming hand you can move the point of contact from fret 10 right back to the saddle to get a big range of sound. This meets my needs.
