Switch FileSystem worker code to use chrome-side bridging

Depends on unsubmitted chrome-side patch.
https://codereview.chromium.org/21997003/

(More cleanup is coming)

BUG=257349
TEST=should break no tests

Review URL: https://chromiumcodereview.appspot.com/21767002

git-svn-id: svn://svn.chromium.org/blink/trunk@156073 bbb929c8-8fbe-4397-9dbb-9b2b20218538