After looking into it some more, I discovered that the IWizard interface is not even called until after the folder structure for the solution (not the projects) has already been created. Since I need to make progress, I've decided to go ahead and switch it to an Add-In to Visual Studio instead of a purely templated process.
I've already had much more luck creating the solution programmatically then adding in the templated projects to my solution. I was able to get around the problem. I've snipped some code but this gives the basic idea.
System.Type vsType = System.Type.GetTypeFromProgID("VisualStudio.DTE.9.0");
DTE2 vs = (DTE2)System.Activator.CreateInstance(vsType, true);
soln = (Solution2)vs.Solution;
soln.Create(PathProjectRoot, SolutionName);
soln.SaveAs(SolutionName);
Thanks everyone for the suggestions.