First off, there's no replacement for displacement, except boost. If you want the power, get the 6.2L, else the 5.3L is just fine.
The short of it all regarding "93 Octane Recommended";
The PCM has two timing tables. One for "Low" Octane (87) with less timing and one for "High" Octane (93, or 91, or 92, you get the point >/=91) with more timing.
If knock is detected, pull timing to match Low table, else use timing from High table. It'll do this periodically.
It all boils down to 4 things;
~Compression Ratio
~Timing
~Octane
~Temps
These newer engines to make more power, use higher compression. These aren't the Cast Iron giant Vortec's of yesteryear, they dissipate heat rather efficiently, and the newer computers are extremely advanced.
Older OBDI prom's had a single timing table, and used Speed Density rather than MAF for calculating Air/Fuel. These are far more advanced than the OBDII 0411 PCM module I rewired into my 94 S10 for MPFI to use a Turbo. These newer PCM's have different tables for different conditions. If low octane is used, the Knock sensor will detect this and cause Timing Retard (pulls timing) until it matches the Lower octane timing table. For a boosted high performance application, by the time this occurs....it's generally too late "Window Block Mod Initiated!"
The concept of using higher octane is to keep predetonation from occurring (ie Spark Knock/Ping). I'd also recommend a catch can for a DI Engine, that shit running through your engine will turn your 93 into 89 real quick depending on how bad you're sucking shit through.
Temps will also effect how well the octane actually works. Winter air is really cold, it's dense and allows for lower octane to be used. These lower temps keep predetonation from occuring. The density of the air is just going to read different according to the Oxygen Sensors and more fuel will be added, but the 87 Octane will perform just like 91+ Octane. Don't believe me, run 87 on a 45°F day, slap it on a dyno, do 3 pulls and record the timing used with HPTuners Pro (or similar). Then run 2 tanks of 93 Octane, go back on same temp day, and do 3 runs and record the timing used. Then come back and tell me I'm right.... because I already know the answer.
The TLDR is;
~Summer (>/=60°F day) 91+ Octane.
~Winter (<60°F day) 87 Octane is adequate, 91+ Octane if it makes you sleep at night.
P.S. steer clear of shitty gas, and if it's your only option, drop in a small bottle of something like Lucas Fuel Treatment first.