Ok, I was able to figure this out on my own after much fiddling.
Method 1: 'proper method'
The issue here is that the incline & decline sections of waveform hit different frequencies. I.e. The incline section hits the odd frequency index's (1, 3, 5,...) whereas the decline section his the even frequency index's (2, 4, 6,...). Due to this lack of symmetry, the PSD will also not be symmetric.
The good side to using this method though is that every possible frequency is touched during the sweep. I.e. the spectral spacing of for this method will be 1KHz based on the previous example.
using an indexed example, the freq index's using this method would be something like : 1, 3, 5, 7, 9, 10, 8, 6, 4, 2 (each number is hit once, but the vector isn't symmetric)
Method 2: 'Time reversal Method'
In this case, each frequency is actually hit twice, once on the way up and once on the way down. Since the incline and decline steps are symmetric, the resulting PSD will also be symmetric.
The downside to this is that the spectral lines will result in being twice the distance. This is because each of those frequencies are being hit twice.
using an indexed example, the freq index's using this method would be something like : 1, 3, 5, 7, 9, 9, 7, 5, 3, 1 (each number is hit twice, but the values are symmetric)
In result, there is no way to have both, a symmetric PSD AND hit every desired frequency.