post a job on here and maybe one of the local lads would be willing to come over and advise you of what can and can t be done, we are here to help if we can
Was it the architect? you may have a case against them. Also who instructed the builder, did the acrhitect put it out to tender and instructed the builder direct? Or did you find the builder?
Responsibility - ultimately the tiler - he should have known not to tile direct to chipboard.
From your information it would seem that the cracks are appearing along the 600mm widths of the Tounge & Grooved chipboard flooring, and the travertine is too soft a material to withstand the movement in the sub floor - especially with the UFH.
Rather than take up all the travertine - unless it is not well fixed - go for a decoupling membrane over the top (ditra or similar) and fix to this, using a flexible adhesive.
Someone will have to be held accountable for your materials and labour costs of the original job and that will be the person you paid to do the tiling.
The only drawback with this method will be a longer warm up period for the UFH.
Hope you get sorted.