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This change simply avoids using RunUntilIdle. I found that RunUntilIdle was
taking 10 seconds for every invocation -- but not on every test run. I'm not
sure of the cause, but using RunUntilIdle is bad practice anyway.

Where possible, I'm using QuitClosure, but we can't do that in all cases.

Bug: 1014706
Change-Id: Icf538182c9572eaa26aa8d5dd6365981555ee1a4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1864418
Commit-Queue: Dan H <harringtond@chromium.org>
Reviewed-by: Carlos Knippschild <carlosk@chromium.org>
Cr-Commit-Position: refs/heads/master@{#707379}