The build trigger that supports ParameterFactory is BlockableBuildTriggerConfig which is a subclass of BuildTriggerConfig which (ironically) is the post-build trigger. Turns out it supports ParameterFactory too so it is trivial to add the jelly ui elements and move the DataBoundConstructor to the complete constructor.
However, post-build triggers are added via the DependencyGraph (using ParameterizedDependency, a subclass of Dependency) and as far as I can tell there's no way to add a dynamic number dependencies to the DependencyGraph. Maybe I'm wrong here and I'd love to see a solution that still respected the DependencyGraph and learn more about Jenkins internals.
A hacky solution would be to solve the feature the other way around: copy the buildresult condition from BuildTriggerConfig to BlockableBuildTriggerConfig. I feel like this isn't really what people want even if it closes the ticket and technically solves the issue in our environment.
Anyways, if folks have advice, I'm happy to keep trying to solve this. Otherwise I hope this helps future people interested in this feature.