On the level shifter:
The basic data stream for WS281x series is less than 1Mhz, but with some fairly tight timing requirements for the Hi and low pulses - down in the 150ns range. That means the ~2Mhz speed of the BSS138 device might not deal well with all of the data waveform, especially the faster bits.
Any of the 74AHCTxxx devices will do a better job ('08,'32,125,245), they’re cheap, fast and reliable.
If the size of the package is too much, the 74lvc2t45 is a tiny package with 2 independent shifters.
Much faster than the MOSFET and still very cheap.
On the scope:
If you’re looking for a scope to properly visualize the actual data stream, you need to start at the 10Mhz devices at minimum. When dealing with pulse widths of 100-150ns you’re talking 10Mhz, and more bandwidth (that means more than 10Mhz) is always better.