You seem well aware that there is a reference implementation for SGP4 in Matlab. Yet you choose to make your own. I've sadly been there, and done that.
Your first problem is to compute XKE, but from the reference you've posted on page 88:
And on page 89:
Since G = 6.67408 × 10-11 m3 kg-1 s-2, GM has units of length³/time². Convert these units to Earth ...
In this answer on Physics stackexchange it is stated that a total of 368 compressor stations along the pipe line should be installed in the case of real gas transport with a given flow velocity of < 10 m/sec.
The pressure drop between the compressors would be from 1 bar to about 0,4 bar.
Pipelines two orders of magnitude shorter on Earth are usually divided into many compressor stations.
But let's take a look at how feasible it is. At the very least, a compressor station would have to provide a pressure greater than the pressure at the bottom of the pipeline.
Fortunately, the pressure calculation needed is unusually simple for a CR3BP
Partial answer. Here's what I have so far. I use Python instead of Matlab, and I "roll my own" dot products, but these plots do look a lot like your plots! I think there might be a missing "2" in the expression for angle, but now that you mentioned you're using 1550 nm light we seem to agree on the size of the Doppler shift though there is still a sign ...