If, in your question, "twin-stick" is a misnomer and you just mean top-down shooter, that's different... My answer is going to assume you do mean "twin-stick."
<sidenote>In the Binding of Isaac, only shooting in 4 directions was a specific design decision. (I can't find a source for that, but I recall Edmund saying it was intentional.) It's worth noting the game does let you curve shots by shooting while you're moving.</sidenote>
If you're targeting a controller as the preferred method and supporting keyboard input, you're going to need to emulate that behavior as much as possible (or write two completely different control schemes into your game and design for both ways of playing).
Two controller sticks is rather precise already. I'm not sure what you don't like about mouse to shoot but I'd reconsider avoiding it. I'd argue that it's less precise than two joysticks since you have to move the mouse to different sides of your character, as opposed to just switching the direction of the mouse. Are you limiting the angles you can shoot in if you're using a controller? If you're not, that's potentially going to suck for keyboard players.
If you must depart from it, consider:
- Allow movement with WASD and shooting in 8 directions with IJKL. Worst (realistic) case is 4 simultaneous letter keys. I don't think that should be a problem for most keyboards.
- It gives you 8 discrete directions to move and shoot separately. It doesn't give you the finer control but is very usable if the game design accounts for it.
- Back in the day, I played the crap out of Robotron on the Apple][ which used a similar scheme (ESDX and IJKM). It was quite playable.
- Allow movement with WASD and lock shooting in the direction that the player was facing when he started shooting. Like Hyper Princess Pitch and Voxatron do.
- If you're moving down and hold shoot, you start shooting down and stay facing/shooting that way regardless of where you move until you let go of shoot.
- Like you mentioned, it does have the disadvantage of having to move toward what you want to shoot for long enough to face that direction and start shooting. It makes running away from a large mob tricker.
- I don't like this scheme myself but in the games I linked above, it does work.
- Allow movement with the mouse and use WASD (or similar) to shoot, like one of the control schemes in Echoes.
- It's a little weird, but it's a possibility. Making the player follow the mouse gives you fine control over your movement while keyboard input still limits your shots to less precise angles.
- Viable if your game is reliant on fine grained movement and less so on shooting.
- Mouse only. (Yeah, we're departing from twin-stick shooter-dom here.) Something like Click-to-move, Shift-click-to-shoot
- It works in Diablo and Torchlight.
- The already suggested forward/backward, strafe, rotate, shoot scheme. But, I'd suggest revising it to not have an extra button to toggle strafe v rotate; add two extra buttons so you can strafe and rotate at the same time. The top-down levels of Contra 3 on SNES did it that way and it was pretty effective.
- Suggested scheme
- WS to move forward/backward, AD to strafe, QE to rotate
- This would also let you translate your controller input the same way (LT and RT to rotate), avoiding significant disparity between your input methods.
Really, it all boils down to how responsive and orthogonal you want your two actions (moving and shooting) to be.