How can I efficiently save multidimensional data that is retrievable by key?

Question

I am doing some simulations in Mathematica, where I calculate a spectrum intensity(frequency) for a variation of parameters in my samples. So in the following image, for example, I vary the charge carrier concentration of a layer and get the following plot:

What I have to do now is do a variation of 5-10 different parameters (charge carrier concentration, mobility, effective mass, thickness, ...) and see the influence of each, depending on each. So I don't want to get 5 of these plots, because in the plot all other parameters are constant; instead, I want to change all parameters and then do e.g. 3D plots to show the influence of any two parameters at once.

As this is going to be a lot of simulations, I want to chuck in a list of values for each parameter, do all the individual simulations over e.g. a week of computation, fill the results in a big n-dimensional hypercube of data and save that. Later on, I would like to be able to extract data from this saved data hypercube in a controlled manner by asking e.g. for all data points with: mobility = 5, effective mass = 3, etc.

As I would then like to use this setup for different samples, or maybe it will be used by other people, or the parameters themselves might also change, ... so I would prefer to use keys instead of just list indices like data[[1,1,1,All]].

I was thinking of making a dataset with every data point added separately like the example from the documentation:

    dataset = Dataset[{
   <|"a" -> 1, "b" -> "x", "c" -> {1}|>,
   <|"a" -> 2, "b" -> "y", "c" -> {2, 3}|>,
   <|"a" -> 3, "b" -> "z", "c" -> {3}|>,
   <|"a" -> 4, "b" -> "x", "c" -> {4, 5}|>,
   <|"a" -> 5, "b" -> "y", "c" -> {5, 6, 7}|>,
   <|"a" -> 6, "b" -> "z", "c" -> {}|>}]

and then I would use all the parameters as key-value pairs to find a row, while the list shown in "c" in this example would then be a list of lists {{x1, x2,...},{y1, y2,...}} with the intensity(frequency) data I want to plot for this parameter set.

Does that seem plausible? It will probably result in billions of data points and maybe I would like to interpolate across part of the data later. Is there a better way to do this?

I would be happy for some input and could not really find an answer to this question via search for multidimensional data and similar requests. Thanks a lot in advance!