While working on my laptop, I found that while horizontally I have a lot of white space, vertically - if I want to drag some task to any context - I usually have to scroll left panel's contents.
Do you think it would be a good option to split the left panel contents into two panels. So while task lists will be in the middle area you will have one panel on the left side and the other on the right. For instance, contexts could be on the right panel - and give user the option what to show and on what panel.