The frequency with which I am coming across the situation where I have to call native 32-bit code from a managed 64-bit process is increasing as 64-bit machines and applications
Pretty much the only answer is out of process communication. You could create a .NET project that is a 32-bit executable that makes all of the 32-bit calls needed and communicate with it via Windows Messages, WCF, Named Pipes, Memory Mapped Files (4.0), etc. I am pretty sure this is how Paint.NET does their WIA (Windows Imaging Acquisition) from a 64-bit process.
In the case of PDN, they simply pass the name of the file they expect as the output, but more complex communication isn't difficult. It could be a better way to go depending on what you're doing.