How to slice a model to ensure at least a certain amount of filament per layer?
I think you have a major XY problem. The amount of material per layer is not what determines the part strength. Unless additional material is placed in a manner that reinforces against the stress you're designing for, it's just wasted. Moreover, infill in particular is not terribly useful this way, as infill has to rest upon the support of existing infill below it. If you suddenly increase infill density at a particular layer, it will not provide any significant additional strength because the added lines will be unsupported and will not bond strongly to anything. Even the next layer above them, and the next after that for quite a few layers, will not bond well because the unsupported lines can just bend downward when the nozzle goes over them, rather than providing a surface for the newly deposited material to press firmly against and bond to.

Generally, infill is not your main source of part strength anyway. I would start out (especially if you can test; if this is a one-off thing, the material cost is not going to be an issue anyway and just go with overkill) by increasing the number of wall lines (wall thickness). Walls generally provide the most strength, and the amount of material used will be proportional to cross-sectional perimeter rather than area, which typically will vary "linearly" rather than "quadratically" (I use these terms loosely since I don't know right off how to make it rigorous - what the independent variable should be thought of as being). My usual default (and I believe Cura's) is 2 walls; I would expect 4-5 to be very strong, and as long as you keep at least 15-20% infill, probably stronger than what you'd get by any increase in infill percent.