2.94 gears with a four speed.

I have a regular case and tail housing sitting on shelf in garage, these are in addition to my complete 2.44 box. I thought all I had to do was buy a regular a833 short tail shaft main shaft and use my non trunion style tail housing with the 3.09 gear set. Is this correct? Ultimately I will have two complete transmissions, one 2.44 box and one 3.09 box.
And sorry, I meant 2.47 23 spline box non bushed not 2.44.