Like desertratt, I worked for years where the company bought Tri-X so you shot Tri-X regardless of the conditons. ND filters might help you stay within shutter speed limits on a bright sunny day BUT in the end, its really about contrast control.
You think 400 is too fast for outdoors/daylight because the contrast gets out of control with blown highlights and empty shadows. Its too slow indoors in the dark because there is simply not enough contrast.
Pushing to 1600 in the dark is really raising the contrast by using a more active developer. I used a LOT of Acufine in those days, a co-worker used Edwal FG7 with added sulfite and we both got usable pics out of 400 speed Tri-X with the camera meters set to 1600.
Pulling back to 200 or so needs a less active developer to hold the highlights back from over development. That's harder to figure out but D76 diluted 1 to 1 at the time recommended for straight D76 is a good place to start.
Bottom line - if you have one film, you need multiple developers to cover all situations.
Takes lots of experimentation to find what you like.