There are a lot of different possible choices for what Email Ext should do when some aspect of the mail implies knowledge of the completed result of the previous build (as for example $DEFAULT_SUBJECT currently does, via $BUILD_STATUS). But it is pretty clear from user feedback that the current behavior—waiting for the previous build to complete—is the least popular choice possible. Jenkins may be running several three-hour test suites on different slaves, so having one that fails after ten minutes wait hours for the “previous” one to complete just so it can report the most precise possible status is crazy.
I would suggest switching back to NONE, which according to my inspection of the code (all uses of Run.getPreviousBuild) would have the effect of treating a running previous build much like a STABLE one, or as if the current build is the first for the project. For example, $BUILD_STATUS would be Successful, Failure, or Unstable, but not Fixed or Still unstable or Still failing. While this is not perfect, it seems acceptable enough; if you have chosen to permit your project to run concurrent builds, presumably you are not terribly interested in build-to-build comparisons, you just want to know how this build turned out.
If there is concern that this behavior would be confusing to anyone, it would be easy enough to add some sort of notification: form validation when configuring the job noting that currently requested elements might vary according to the previous build result (if the concurrent builds checkbox is also ticked on the project’s configuration screen); or a warning in the console output when email is being sent but the previous build is still running (possibly restricted to token macros which were checking that previous build); or notification in the email itself, e.g. having $BUILD_STATUS read Successful (previous build still running).
The plugin could also skip over still-running builds and consider only the latest preceding completed build, though it is not clear this is any more intuitive: you could for example get two Fixed mails in a row.
I would volunteer to file a pull request for one of these behaviors if the plugin maintainers agree that a change would be desirable. (Of all the possibilities, a warning in the console output seems easiest.)
I'll research this.