Next, when I'm printing a negative with very little actual highlight I'm finding it difficult to judge the low contrast exposure, as anything but the brightest of highlights seems to get changed dramatically by the high contrast exposure. I'm wondering whether this means I should try testing for high contrast first then dial in the highlights afterwards for these sorts of prints...
That is exactly what you should try.
In essence, the first test should result in a print that is almost final, while the second test is used to finalize the print.
A subject which has large (or at least important) areas of shadow and small areas of highlight will benefit most from carefully adjusting the contrast and density of the shadows. The high contrast filter has a much more direct affect on those shadows.
A subject which has large (or at least important) areas of highlight and small areas of shadow will benefit most from carefully adjusting the contrast and density of the highlights. The low contrast filter has a much more direct affect on those highlights.
Keep these factors in mind when you determine the order of your tests.
Also keep in mind though that you can often benefit from additional, localized, contrast adjusting burns and dodges. As an example, if you use a low contrast filter to bring out density in the otherwise white sky, consider also adding to the sky area a localized high contrast burn, to see if that adds wanted definition and detail.