Due to the lack of locking, there was a chance the the update thread
`context` was retrieved just before the `flushContexts` call, followed
by `.Refresh()` being run while the blocking behaviour was invoked.
This can be seen in test failures such as
https://ci.appveyor.com/project/peppy/osu/builds/39859786/tests.
As an aside, I tried multiple different methods to avoid `lock()` on the
update thread but they felt flaky. The overhead of lock when there's no
contention is reportedly around 30-50ns, so likely not of concern. We
can address it at a later point if it becomes one.
Also refactors the whole method to generally clean things up. One more
important fix is setting the frequency on the channel before starting
playback, so avoid the frequency potentially being adjusted after the
playback is already started.