One approach would be to avoid sampling at all, by using boolean geometric operations to find the exact shapes of visible polygons within a pixel, then using their color and areas to calculate their combined contributions. I expect the calculation involved will be impractical relative to multisampling, though.
Another approach would be sample exactly once per pixel or, equivalently, render the polygons without antialiasing. Naturally, that would eliminate the show-through of hidden geometry at the expense of the accuracy of pixels around polygon edges. You might then be able to approximate the antialiased values by a post-processing filter, maybe guided by the presence of edges, although doing so will introduce its own set of artifacts.
And if you consider "one sample per pixel" to be a budget over the entire image, you could sample the polygons more densely near polygon edges and more sparsely elsewhere, using nearby samples to approximate the values of pixels with no samples.