Race condition between MTP extensions using ITestHostProcessLifetimeHandler

I'm the author of ReportGenerator which you might be familiar with.
I want to provide a version of ReportGenerator which can be used directly as a MTP extension.
The idea is, that you can use both Coverlet.MTP and ReportGenerator within the MTP platform.
Coverlet collects coverage information and ReportGenerator should generate the corresponding report.

On the command line it would look like this:

dotnet run --project MyProject.csproj --coverlet --reportgenerator

or

dotnet test --coverlet --reportgenerator

Now the problem:
Both Coverlet and ReportGenerator register an out-of-process handler ( ITestHostProcessLifetimeHandler.OnTestHostProcessExitedAsync method).
This is the last method in the execution order (see docs).

On my machine the ReportGenerator handler gets executed before the Coverlet handler. Therefore no coverage files exist (they get generated by Coverlet after ReportGenerator has finished).

Is there a supported way to control ITestHostProcessLifetimeHandler execution order between extensions?
The ReportGenerator handler should be executed after Coverlet.

@Bertk from the Coverlet team suggested to reach out to @Youssef1313.
It would be great if you can take a look.

If required, I can provide a sample repository demonstrating the issue.

Start with ITestHostProcessLifetimeHandler.OnTestHostProcessExitedAsync and the linked MTP extension execution-order documentation. Reproduce the interaction using the shown Coverlet and ReportGenerator command examples, or the sample repository if provided. Done means identifying whether a supported deterministic ordering mechanism exists and documenting or implementing the agreed behavior.