The 5.3 is a smaller LSx based motor, Personally I would just swap in a 6.0 or 6.2 or even a custom 400+ cube LSx engine. (427, 454 if you really want power) Or add a supercharger like the Edelbrock E-force or Magnuson TVS1900 or milled heads to raise compression.
Do you need more low end torque or more high rpm power. I would assume more low end grunt for the 37's.
Personally, I have a 6.2 LS3 engine in my garage, if I had an alpha I would swap that in for the easiest power gain. The truck L92 engines can be found for under 2 grand on occasion (used out of Escalades and Denali SUV's) they would make an improvement without the complexity of a supercharger and keep the stock drivability without going to a large camshaft and loose low end torque.
Ryan