Template parameters for powershell script in Visual Studio project template?

Question

I have a project template that contains a powershell script called BuildStandard.ps1. Inside that script is the following excerpt:

Invoke-psake -buildFile $psakeScript `
            -parameters @{
                "solutionFile" = Resolve-Path("..\$SpecificSolutionName$.sln")
            }

When a new project is added using the template, I want the $SpecificSolutionName$ parameter to be replaced with, well, the solution name. Only problem is that this content from the .vstemplate file isn't cutting it:

  <TemplateContent>
    <Project TargetFileName="PsakeInstallTestBench.csproj" File="PsakeInstallTestBench.csproj" ReplaceParameters="true">
      <ProjectItem ReplaceParameters="true">BuildStandard.ps1</ProjectItem>
    </Project>
  </TemplateContent>

What am I missing?

EDIT: I've verified that if I replace $SpecificSolutionName$ with $safeprojectname$, the parameter is replaced. I'm beginning to wonder if $SpecificSolutionName$ is available only for solution-level templates. Is there a workaround for this?