Hy Sam, I believe you won't be able to do the rest calls without a connector.
The reason why is explained here in this old topic:
While it perhaps might be possible to cobble something together without add-ons, the fun of working through getting RID of "no add-ons" stuff from predecessors is showing me the beauty of plugins in this environment.
If you build something and make it work, you become responsible for KEEPING it working through API changes as the versions migrate. If you do it with plugins then it becomes a SEP (Somebody Else's Problem) as the vendor then is keeping up with it and you just keep stuff updated.
The alternative is you could be stuck on a version of JIRA for as long as it takes to update anything you cook up even if it happens to be <gasp> a buggy version.
My $0.02 worth
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