I’d suggest exporting the HOMEBREW_NO_INSTALLED_DEPENDENTS_CHECK=1 environment variable to remedy the slowness with update: true. According to the manual,
If set, do not check for broken dependents after installing, upgrading or reinstalling formulae.
… which seems reasonable to use in Travis CI because a lot of packages are preinstalled for user convenience, but the typical project will only need some of them (or, even better, will explicitly list its top-level dependencies in its .travis.yml or .Brewfile).