Laurent,
Can you be a little more specific about the tuning changes and what happens to the playing action (e.g describe one tuning change to another and the action changes - all strings, some strings etc).
What arch/dome was in your top? You could leave the centre of your tops a little thicker and feather out from there and brace accordingly to keep the top responsive.
If you play in a lot of tunings it can be a little tricky, especially as they have different "balances" - the DADGAD tunings low at the extremes, but the C tunings having the second sting high at C and the 5th and 6th down to C and G, and finding the right string gauge combination can be challenging. Colin S advocates a guitar for each tuning with suitable string sets
I move hugely between tunings and also have the twin carbon fibre re-enforced necks and don't have issues of action changes. It could be I not as sensitive to them as you and they are occuring, but my tops in the middle tend to be nearer 0.12" and much thinner at the edges, and I also have pretty big arches in the top especially side to side.
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Dave White
De Faoite Stringed Instruments". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010