Thanks for the response Daniel.
I now see that this is not a folders plugin related issue, but appears to be a Jenkins version issue.
My initial efforts were on a Jenkins OSS version 1.569 using Rebuilders plugin version 1.21. This was a folder-less setup.
My folderized tests system is a Jenkins Enterprise version 1.574 using Rebuilders 1.21. This is the folderized setup.
Since the Jenkins versions were pretty close, i didn't expect different behavior based on the Jenkins version, but in fact that seems to be the case.
To simplify the test i made two new free-style jobs at the top level of Jenkins instances.
"Trigger Source" has one String parameter "TEST_PARAM" default value = "Got it?".
"Trigger Target" job is just a a new free style with no changes.
"Trigger Source" triggers "Trigger Target" with Add Paramters/Current build parameters.
After one time launch of "Trigger Source" on the 1.569 instance, doing Rebuild Last on the "Trigger Target"displays the TEST_PARAM passed in, but on the 1.574 Enterprise instance, rebuilding the "Trigger Target" job does not display or pass the previously passed in TEST_PARAM.
I'll do some additional testing on the Jenkins versions in-between these two, and also OSS vs. Enterprise to see if i can isolate where the change occurred.
Has nothing to do with folders or build flow.
The current behavior seems sane, as it only provides parameters currently defined on job (i.e. its contract). This is the resilient option in the face of job configuration changes between the time a build was started and when a user tries to rebuild, so that when a parameter is removed or renamed, it will no longer be part of "rebuild".
Considering both behaviors, the current one seems to be less surprising.
If a build script accesses certain parameters, why not just define them on the job running the build script?