I would recommend you send your engine to JDM engineering and have them install the parts. Either way, it'll be pricey. I paid around 18k for my engine with upgraded cams and all valve train components. If you don't want upgraded cams, that will save you a good amount.
You can do what I did and do the JDM engineering upgraded rods and pistons
https://www.svtperformance.com/threads/built-engine-time.1196498/
https://www.teamjdm.com/2013-2014-gt500-5-8l-aluminum-shortblock-1200-hp-rebuild-kit/
3.73s doesn't make the car work harder, if anything it makes it easier on everything. 3.08s would be a different story.
What all do you have done to the car? What fuel are you using? Sounds like your tuner didn't know what he was doing if you "nuked a piston"
If the 99/01 cobras take a specific thermostat I would replace that as well while I'm in there with the correct one. I know the GT500s take a special thermostat and you'll have issues if you don't use the right one.