Mylyn
It seems it is possible to use Eclipse Mylyn with our mifosforge.jira.com Atlassian Studio JIRA:
In addition to (obviously) Mylyn itself, you need to install the Atlassian Connector for Eclipse, if it didn't already come with your Eclipse/Mylyn. It's probably possible to install that via the "Install More Connectors..." button in the Add Task Repository UI?
Now in the Tasks List view (shown e.g. by switching to the Planning perspective of Mylyn), click that first icon and Add Repository... in Select a task repository type pick the "JIRA (supports 3.13 and later)". If you don't have that, it's probably available via the "Install More Connectors..." button?
For Server, use simply https://mifosforge.jira.com, for User ID & Password your Mifos Forge Profile Username and Password. When it says that "The repository location reported by the server does not match the provided location.", it seems to be safe to "Keep current location", and not let it turn the https into http. – Use the Window > Show View > Task Repositories, if you need to find your JIRA Repository Settings again.
You can then create New Query, typically e.g. "Assigned to me (All Projects)", and open JIRA issues straight in Eclipse, update them, attach Task context to them - use Mylyn!
FYI: EGit integration for Mylyn is being actively worked on.
PS: Page written up upon discovery that this appears to basically work; hasn't been extensively tested, yet. Mylyn was known to have issues with (highly) customized JIRA instances (e.g. used to be unable to handle custom workflows), but as mifosforge.jira.com is relatively standard (and Mylyn made progress), should be OK? Please do not hesitate to update this page with further findings.