In case you were wondering about the state of searches for strings on hardware store web sites, here it is.
Lowes and Home Depot: Absolute shit. No filtering or ordering search results by size. You can search for a 1" spring, but you can't specify that's the length you want, not the width.
McMaster and Carr: Excellent as always. Searching for "extension spring" gets you to a
list of spring types, which you can follow to
types of extension springs, and finally a
list of extension springs with loop ends sorted by length.
If you go to a product detail page, you can download a 2D or 3D diagram of the spring. Unfortunately, you have to buy a pack of them, and shipping is a minimum of $10, so I'd have to pay $20 to get a single spring.
Grainger: Also good. Lets you filter by free length (the length of the spring when at rest) and extended length (the length when it's stretched to the max). Same shipping cost problem, though.
I ended up searching DuckDuckGo and buying one from eBay for a total of $11 for this 1.125" spring. That's a lot, but I guess I can think of it as paying that much to repair the sostenuto pedal.