I was considering more about what I said above, about how the 3sgte block may bolt to the 3sge (longitudinal) transmission. I was figuring before that the blocks were likely the same, just as the 2jzge and 2jzgte blocks are nearly identical. It seems that the 3sge was available as a straight longitudinal layout and as a transverse slanted layout. The 3sgte was only available as a transverse slanted layout, so I don't think using the 3sgte would be possible. Not only would the longitudinal transmission likely not bolt up, but the oil system might be compromised rotating the block vertical if there are differences made to the block to accommodate the slant setup.
3sge longitudinal
3sge transverse
3sgte transverse