With Greenshot 1.2.9.84 and later (currently in test, release candidates come soon) most imgur issues are solved. (For now, until they change stuff again).

Unofficial versions (not released for public) can be found here:
https://github.com/greenshot/greenshot/releases

Is there a way to run the two in parallel so I can check the beta when the stable fails to run?
As I said, this problem happens intermittently (but still often enough to be annoying)

Can you please try if this is solved with the fixes I made for the next release?

You can find our "beta" (it's marked unstable, as it needs testing) here: https://github.com/greenshot/greenshot/releases
Download Greenshot-UNSTABLE-1.2.9.40 or later.

And let me know if that works for you.

Going to greenshot->imgur->configure shows the 'Communicating with Imgur' window as well. When cancelling it, getting this dump:

Software version: 1.2.8.12-RELEASE-cab854b7229994fc9e4deaccd47885df500d7e1a (64 bit)
.NET runtime version: 4.0.30319.42000+
Time: 2016-07-14 12:10:08 -07:00
OS: Windows 10 (x64) 10.0 build 10586 revision 0
GDI object count: 143
User object count: 132

Exception: System.Threading.ThreadAbortException
Message: Thread was being aborted.

Stack:
at GreenshotPlugin.Controls.PleaseWaitForm.ShowAndWait(String title, String text, ThreadStart waitDelegate)
at GreenshotImgurPlugin.ImgurConfiguration.ShowConfigDialog()
at System.Windows.Forms.ToolStripItem.RaiseEvent(Object key, EventArgs e)
at System.Windows.Forms.ToolStripMenuItem.OnClick(EventArgs e)
at System.Windows.Forms.ToolStripItem.HandleClick(EventArgs e)
at System.Windows.Forms.ToolStripItem.HandleMouseUp(MouseEventArgs e)
at System.Windows.Forms.ToolStrip.OnMouseUp(MouseEventArgs mea)
at System.Windows.Forms.ToolStripDropDown.OnMouseUp(MouseEventArgs mea)
at System.Windows.Forms.Control.WmMouseUp(Message& m, MouseButtons button, Int32 clicks)
at System.Windows.Forms.Control.WndProc(Message& m)
at System.Windows.Forms.ToolStrip.WndProc(Message& m)
at System.Windows.Forms.ToolStripDropDown.WndProc(Message& m)
at System.Windows.Forms.NativeWindow.Callback(IntPtr hWnd, Int32 msg, IntPtr wparam, IntPtr lparam)

Configuration dump: