One critical feature is the ability to take a run, say a failed run, and tweak the Jenkinsfile, and run it again, without having to change the Jenkinsfile and push and trigger a build.

this is CRITICAL for making Jenkinsfile practical, a feature which is heavily used by those that know about it.

This can work by having an option that pops over "Replay and alter pipeline" (it could be grouped with "replay", just an option to tweak the Jenkinsfile).

An ACE based editor could then popup allowing small changes, and then run it (in which case it goes immediately to the results/running screen for that new run).

Once a user is happy with the result, it is up to them to grab the changes and paste them into their Jenkinsfile, so making it clear that they can click and view the Jenkinsfile once their replay has finished is also important.