The Marathon bullets are utterly unreliable-- all are claims of antiquities dealers in the C19th (already critiqued by the Swiss scholar Visscher, I think).

Tissaphernes: yes, that's after 401 BC (he's the guy who fought the Greeks after Kounaxa. That's the argument of the guy who published the first known Tissaphernes bullet, Clive Foss, in JHS 1975. Two more Tissaphernes bullets have appeared on the antiquities market recently).

Just to make the argument a bit clearer: Tissaphernes is the satrap, in office in the late C5th in Ionia (411 BCE), displaced in 407 BCE, returned to office in the last years, then executed in 395 BCE. Now when fighting against the Greeks in Babylonia, the Persian troops didn't have sling bullets in 401 BCE. But there are sling bullets with Tissaphernes' name. So, perhaps, he learned the idea in 401 BC and applied it to his troops in W. Asia Minor after that. Of course, maybe Greek troops in Persian employ in Ionia say in 411 BCE did know how to sling lead.

The point still remains: not clear when sling bullets in lead start to be used, probably very end of the C5th

really appreciate the input here folks! Am tempted to go the full hog and give it a go myself. I live on the South Downs (Sussex, England) so have plenty of space to practice.

thanks again!

Do you have good slinging stones on your beaches, or is it all chalk ?

You have no real reason not to try it at least once, just for research. Start up cost is practically nil and some designs for making slings are so simple that anyone could make them. As much as we can help you, it's no substitute for actually feeling what your character will.