Barke Vienna, Barke Pils or….?

[Protos]

Maybe limiting myself to just one of the malts is a pointless exercise in self control.

That's true.
My own takeaway from a similar experiment on self-restriction was that it was too much of a Taliban thing to limit myself to just one grain and it felt a bit silly.
In my book, minimalism is a virtue. After all, that's how beers have been brewed for centuries. Back then, they had no 50 shades of fancy Crystals and Biscuits we have today.
When surfing recipes for my next brew, I pass by any which includes more than 3 malts. There might be cases where more than 3 malts (or more than 2 hops) are REALLY needed for a recipe (even 5-malt grists are not ruled out in exceptonal cases) but there must be very serious grounding behind each extra grain or hop introduction.

You can brew any traditional beer having just 4 malts in your closet: Pilsener, Münchner, Pale Ale and Black Patent.
And just 4 essential hops: Kent Golding, Hallertauer Mittelfrüh, Saazer and Cascade.
You don't even need any Wiener, since you can approximate it with Pilsen+Munich. And you don't need Crystal at all, even in English beers ("Especially in English beers" - the knowledgeable would add).

That's what might really be called a wise limiting without compromissing the process.
A "Wiener Pils" is possible but it's just a compromise, of course.

However, if you're set on the Single Malt Challenge, then I'd suggest Vienna.