From my research earlier I found that;
KE30-55 Auto had 4.3
KE30-55 Manual had 4.1
KE36 Manual had 4.5
KE38 Manual had 4.3
KE30's ran Jap diffs whereas KE55's had Borg Warners.
Also, i'm not sure whether I remember if you were building a Corolla junior sedan, but if you are coming close to registering it, register it as a KE30 or KE35; it leaves you open to more diffs, as you can get into complications fitting older diffs on a newer car legally under Junior Sedan guidelines.
Anyways man, see you on the track.
Dan