This is the new backend in the ws281x-systack branch: RIOT/drivers/ws281x/busywait.c at ws281x-systick · maribu/RIOT · GitHub
You can select it by using USEMODULE += ws281x_busywait, but actually, the dependency logic here should select that backend automatically when you just use USEMODULE += ws281x.
The SPI Mosi pin abuse is also something interesting, will try it if I can do something.
It should be possible to write a backend for that even now, but the user would have to specify an spi_clk_t value to use and the actual frequency in Hz this constant would select. Once the SPI API change is in, this would no longer be needed, as the driver could just use the API to obtain the actually used frequency.