Luce,
My opinion based on experience,,and I' ve read where some others with loads of detector experience have written I value and respect.
Most instances,,,A 10-11" coil is where an op will get peak performance depth wise on coin sized targets.
Now a bigger coil may get you say a deeper half dollar or silver dollar.
You will see where some folks find some rather deep coins even dimes while using a bigger than stock sized coil,,,but the question is what would the deeper say dime have sounded like if the stock sized coil would have been used and swept.
Bigger coils cost loot too.
Bigger coils are generally heavier too,, can make detector weight/ balance very uncomfortable.
I am not a fan of using bigger than stock coils--- now they do it seem have a place for say hunting at a beach and maybe a sports field.
IMO your loot would be better spent upgrading to another detector,,and yes this means you may take a hit find wise for a period until you get adjusted to your new to you detector.
And really a lot of " not so much increase" in overall depth on coin sized objects,,
mainly associated with bigger coils seeing more ground vs stock sized coils,,,hence no real depth gains-- moreso ground coverage,,,and don't forget your detector's separation/recovery in around trash and iron-- suffers greatly.
Take a look at what sized coil comes on many detectors,,by the different manufacturers--White's, Fisher, Minelab, Garrett etc..
It is not a coincidence to see them as stock coils offer coils like 11" round dd, 7x11" , 8.5x11".
Cheers