You don't need a complex airplane for the SEL ATP. You've already shown you can handle a complex airplane during the commercial checkride. You can fly the SEL ATP ride in a J-3 if it has the boxes to shoot three diiferent types of approaches. Most CE-172s fit the bill. Certainly no shortage of them.
I think the reason few puppy mill schools do the SEL ATP is "what's the use?" There's no reg requiring a SEL ATP. I did mine because the 24 months on my written has coming up and it was cheaper (and easier) than a MEL ride.