I know that I can edit my TaskPaper files using Vim.
But what about using Vim commands in TaskPaper itself for navigating and editing text? Is this possible using some plugin or is this something (given that there is some user interest) that could possibly be on a roadmap? 
You might be able to set that up with a macro utility like Keyboard Maestro.
Sorry I think this is unlikely anytime soon.
TaskPaper does use NSTextView, so any cocoa hacks (such as custom keybindings) should work with TaskPaper… but NSTextView is non-modal, so I don’t think you’ll ever get very close to full VIM keybindings.
Just go get Karabiner and give yourself a Universal Vim mode.
It might be just what you are looking for.