MojoLPM: Removing nested RunLoops from CodeCacheHost fuzzer.

The bug that originally prompted this change has been fixed, so this
is now just refactoring.

This refactors the CodeCacheHost MojoLPM fuzzer to avoid depending on
nested RunLoops. This is also part of the preparation for a future CL
that will abstract out a lot of the common testcase code that's
currently shared between each of the existing MojoLPM fuzzers.

Change-Id: Ia822e61e870e708cc268c460e8044c78b1352e85
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2862775
Reviewed-by: Jonathan Metzman <metzman@chromium.org>
Reviewed-by: Daniel Cheng <dcheng@chromium.org>
Commit-Queue: Mark Brand <markbrand@google.com>
Cr-Commit-Position: refs/heads/main@{#922868}