Nitrous
I would remove exhaust cooler, install new oil cooler/flush coolant, stc, clean the turbo. Then get custom non-studded tunes. The factory air filter is a good filter for stock and slightly modded 6.0s imo. Wait to replace the exhaust for when the cab comes off for studs, I have never installed a down pipe with cab on so it may be easier than I lead myself to think.
The down pipe isn't terrible with the cab on.
OP, I would start with a coolant filter, "fix" the EGR, blue spring, exhaust and a tune from Matt.
Its pretty easy if its a two piece down pipe.
I ran my 6.0 for two years without studs with an AFE intake,blue spring upgrade, EGR deelete, 4" turbo back exhaust, powermax, and custom tunes on an SCT from Total Diesel Performance aka Tony Wildman.