Confusion regarding variable light speed theories

Einstein and others have thought about VSL theories. But I am unable to understand how VSL theories can be consistent, for the following reasons:

Don’t we need some mechanism (like Einstein Synchronization) to synchronize distant clocks? For example, if speed of light varies with time or space, what do we use to synchronize distant clocks? Without synchronization, how can we measure lengths and time intervals accurately? Can we even measure speed of light, in the first place?

Couldn’t we just replace a VSL theory with one in which light speed is constant, but lengths and time intervals are varying? Using VSL theory seems unnecessary (exactly in the same way luminiferous ether was unnecessary). Thus, it seems like VSL theories would be difficult to test experimentally.

But, of course I must be mistaken since a lot of physicists have worked on VSL theories. Can somebody help me with understand this?