Characteristic Impedance of Multi-Dielectric Coplanar Waveguide
You're very unlikely to find any simple calculator that will solve these problems.
The way the simple calculator works is that at some point someone did some EM simulations (for example finite element method [FEM] simulations) of a trace geometry, with some variations in the dimensions. Then they found an interpolating formula that fit the simulation results and the calculator uses this fitting formula to produce its results.
With 7 dielectric layers, each with a dielectric constant and height that can be varied, there are simply too many free parameters to make it practical to generate a fitting formula for this geometry.
If you had just a couple of materials with fairly close dielectric constant (say an FR-4 core and FR-4 prepreg, with \$\varepsilon_R\$ of 4.5 and 4.7), you might get adequate results by just averaging the dielectric constant.
But with your widely varying materials (\$\varepsilon_R\$ ranging from 3.5 to 5.1), you will probably have to do the full simulation yourself to get an answer. General EM simulation tools like HFSS from Ansys and Microwave Office from AWR can do this simulation. It looks like Polar (a field solver specialized for finding transmission line impedance) now supports some geometries similar to what you need, but it's unclear if they support as many layers as you have in your problem.