Migrate some //remoting tests off QuitCurrent*Deprecated()

Change-Id: Idb59b065a592de026cbdfe13e820ffabb7bf0674
Reviewed-on: https://chromium-review.googlesource.com/1239713
Commit-Queue: Wez <wez@chromium.org>
Reviewed-by: Joe Downing <joedow@chromium.org>
Cr-Commit-Position: refs/heads/master@{#593461}
2 files changed