I think the "turnable" approach would be fine if it included an extra roll control. Probably preferable due to the ease you point out; this overcomes the limit you point out.
My personal preference, and how I've set up my visualization engine (For chemistry vis projects and similar): Move the camera; not the object. FPV controls, plus a roll axis, with crouch/jump for up/down. Works best with a videogame controller, but FPS standard + Q/E is fine too! Full control, and intuitive if you've played those sorts of games. This is full 6 axis.
My personal preference, and how I've set up my visualization engine (For chemistry vis projects and similar): Move the camera; not the object. FPV controls, plus a roll axis, with crouch/jump for up/down. Works best with a videogame controller, but FPS standard + Q/E is fine too! Full control, and intuitive if you've played those sorts of games. This is full 6 axis.