Spin up their own unaffiliated union?

A few googlers teaming up can presumably afford to pay some labor lawyers to draw up the paperwork and guide them through the process. It'd also leave googlers' more in control of their destiny than quickly becoming a franchise of a larger union.

With the hundreds of members they now have, they could cover a few staff and/or consultants. Maybe even with some sort of loan to the union for spin-up costs that could be repaid from future dues if successful?

UAW is another common choice, but they have a terrible track record of squashing workers rights in the University of California system. (Read up on the 2020 UC Santa Cruz wildcat strikes, or when they negotiated to reduce health care coverage for female grad students and also forced student salary caps through a decade or so ago.)

Why work with any of them?

The IWW for one.