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What you are describing is a stripline. The width of the strip and the width of the sustrate determine the characteristic impedance of the strip, or track. The distance to each ground plane need not be equally spaced, but it will all effect the impedance.
It is easier and cheaper to just keep the stack up with eaqual spacing. You can find stripline calculators on the net.
Some complex stack ups have different substrate materials between layers, but these are pretty specialised applications.
see, if the adjacent layers are reference layers say power or ground. the signal travels on the skin of the trace and if u have different dielectric thickness on either sides of the trace the signal transition will not be same for rise and fall.
it is accepted that the impedance is going to vary. but u also need to care about the capacitance. the trace to power and trace to ground capacitances are going to be different for the stack up that has different heights of dielectric on its either sides.
Do you need the high speed lines to be impedance controlled? No need to be that complicated. Just tell us which lines to be controled, we'll adjust the width and choose the right prepreg material to meet the impedance.
the impedance could be controled within +-5%.
It seems you prefer to take an impedance control on your circuits. Yes, you may calculate the impedance value depends on strip widths and spacings. However, the pcb fab generally will do a second caculation based on their fab machine and fab flow. Anyway, don't worry, the difference normally is very small. All in all, ask the fab shop engineers for help is needed, or you probably meet some difficults when receiving the final prod.