I'm working on this very problem! However, I am coming at it from a different perspective. I am developing a prototype "full squat" composting toilet that leverages the Lovable Loo design.
The dimensions of such a toilet are ellipsoid (not circular). Here's a typical squat toilet model:
A hole of this shape would necessitate an elongated toilet seat and based on my rough calculations, an off-the-shelf seat would work.
I discovered that there are such things as
oval plastic buckets with tight-fitting lids:
source
The catch is that I can't find anyone in the U.S. who carries them, so they would need to be ordered from overseas (unless and until someone manufactures them here and/or they otherwise become more widely available.)
With the oval bucket, an elongated toilet seat box would just need to be a few inches longer to Jenkins' Lovable Loo round bucket model.
I've got some design issues that still need to be worked out with the squatting part, but the other pieces fit together.
After prototyping, if I like how it works, I'd be willing to order a large amount of those buckets (5000 e.g.) A given family would only need say 4 of them and they look to be as durable as the round ones.