I've got an itch to make some mail but the round rivets provided with the pre-made links are really awful even if I'm willing to turn a blind eye to other historical inaccuracies. Is there a better off the shelf rivet option or at least an easy DIY one?

A piece of wire? From Vegard Vike's Ring Weave, a section of a ring from C 2616, Møllerdalen, Buskerud, fragment of a mail hose (chausse): The round wire ring is about 1mm diameter with a 0.3-0.5mm diameter "rivet".
http://www.themailresearchsociety.erikds.com/pdf/tmrs_pdf_11.pdf

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I guess it comes down to making a custom rivet setting tool then.

Some of these examples are better known than others, but it seems any shape of tong or pincer would do as long as the recess isn't too large.
http://www.nuernberger-hausbuecher.de/75-Amb-2-279-26-v
http://www.nuernberger-hausbuecher.de/75-Amb-2-317-10-r/large
http://www.nuernberger-hausbuecher.de/75-Amb-2-317-92-v/large
http://www.nuernberger-hausbuecher.de/75-Amb-2-317-103-r/large

Thanks, Eric. (Also corrected my post--how did that code closure end up in there !?)

Mike R: would a set of riveting tongs (such as the ones sold by HE or Andre) not work for what you want to do?

(This is less a suggestion, and more a question out of ignorance :) ... I've not used them, and don't know what result they give versus what you want to end up with.)