[MemProf] Make --synchronize-timestamps mode fully synchronous.
[MemProf] Make --synchronize-timestamps mode fully synchronous.

Due to insufficient lock scope there was still a race in recording which could lead to races during playback.

BUG=

Review URL: https://codereview.chromium.org/1770223003

google/syzygy,google/syzygy,Eloston/syzygy,Eloston/syzygy,google/syzygy,google/syzygy