There's no "raw copper float" in our part of the USA. But just taking a stab at your question in general : How big can the bigger pieces get ? Eg.: domino sized ? fist sized ? soda can sized ? etc.... If there is enough of them that start to border on the size of a playing card (from a deck of cards, like Ace of spades) : Then how about using a 2-box machine, like a TM 808 ?
They will not see all the nuisance smaller items. About the utmost smallest item it will detect is: A domino or silver dollar sized object, if you held them "just right", and super tuned it, holding close to the ground. But realistically deck-of-card sized, or soda can sized, or larger. If there's enough of those sized items to angle for, and you are growing weary of the coin and pebble sized copper, then perhaps this is an option.
Some people might say you can tell big vs. small by just going by your audio strength and sound. There's a bit of truth in that. But at the end of the day, it will wear you down. Because you'll perpetually be asking yourself: "What if this small beep is actually a big copper piece, that just happens to be very deep, such that it simply *sounds* small ?" And you'll find yourself perpetually digging a bunch "just to make sure".