This is a reland of https://codereview.chromium.org/2102613002/ .

See https://goto.google.com/ljfzu (Google-internal) for more context. Summary:
- the only builders with chromium checkout affected by this are on chromium.fyi
- we can't clean up old cache directories before switching to new ones

Also see https://goto.google.com/oyxwm why so short directory names are OK.
Similarly https://codereview.chromium.org/2061213002 .

BUG=623575

Review-Url: https://codereview.chromium.org/2102403002