My 2 cents...yes a tuner will make a big difference on your 6.2
I've used 5* Perf Tow tunes for around 7yrs on my F150 with a SCT tuner and it works great for me.
The thing is you will drop around $350+ alone just for a tuning device that will come with generic tunes for your specific application-which is fine> IMO
No it won't increase your towing payload capabilities, only enhance your towing experience.
To me it sounds like you are fine currently with what you have running 91 octane. Why spend the money for a tuner etc...
It's up to you....or should I say the " other half" -lol
when it comes to spending money on modifications to your F250 gasser.