To give a contrasting viewpoint, I don't think you need to change your per-program keybinds. I've used vim with qwerty, dvorak, and Workman. I never rebound hjkl or anything else. The letters are in another spot, which you have to get used to... just like you're already doing to type words at all. Plus, in the case of vim you'll probably use stuff like e and w and search to get around faster a lot of the time anyway.

As for games, I always rebind everything, or play with controller. It's a one-time thing per-game and then you're comfortable and can also use an in-game chat without trouble. Plus you can use this chance to switch to ESDF-style (the equivalent in your layout, so RSHT for me) controls from WASD controls so your fingers can be in the normal homerow position.