Sounds like all you need is à plugin to call makefile targets from vim.
It's also near impossible to get I J K L working as the cursor keys in VIM without having some major interference.
You could write elisp functions for your tasks and bind them to your prefered keys, with or without Evil.
With evil-mode, there's no excuse not to try it even if you find Vim's way of controlling input superior (which it as well may be).