1995 tahoe motor swap to newer 5.3L

[AtlDiminishedValueApprsr]

I have a 1995 Chevy Tahoe I purchased with a blown motor. Can I replaced that with a late model 5.3L with the shift sequence it has where every gear has power? The motor and trans in my 2014 Sierra is what I have fallen in love with so I wanted to see my options with replacement. I do not have unlimited cash to do this so if it will cost a large amount then what are other options to replicate the new shift sequence and power? Any input is greatly appreciated.