I finally figured out how to get it to work, and as I suspected (based on previous experience with Impulse itself not running properly under a non-admin account), it appears to be a permissions issue. I set the Properties of the Impulse shortcut to run as Administrator, though Impulse gives you a big warning about running it as Admin. The reason for the warning is probably because once Impulse runs as Admin, any other process that it starts also has Admin rights. So if you use Impulse as your Stardock application launcher, all those applications run as Admin.
Sure enough, I was able to launch the current alpha of LogonStudio Vista with success under those admin rights.
As an aside, I tried to run Impulse as Administrator when I was running it under the limited User account, but it wouldn't work right until I upgraded my User account to one with Admin rights. This pretty much destroys the benefits of UAC and the higher security of Vista. UAC was specifically designed to encourage developers to write their code to ask for elevation when needed, but also to run well without admin rights. I hope that Stardock will work on getting Impulse working as it should under Vista.