Not sure I understand you completely, but here's a few thoughts:
1440x1080 is an anamorphic aspect that accommodates things like HDV 1080 (or DVCProHD 1080), which is then displayed by the codec at 1920x1080. Otherwise, there's no such animal as 1440x1080 as a standard size for anything other than those uses.
An HD projector will only project 16:9, and will typically have a setup menu to display 1920x1080 or 1280x720.
An HD image projected onto a 4:3 screen can only appear letterboxed when the projector is adjusted to fit the image horizontally. There's no such animal as a 4:3 HD image. HD is always 16:9. To fill a 4:3 screen vertically with an HD image, you'd have to crop off the image left and right (pillarboxed) and position the projector to accommodate for that.
What is your source footage? If it's an HD format, why use a 4:3 screen? Let us know that and maybe there's a better answer.
Clay