One of their homes is Hall Manor located in Westchester County New York so perhaps their museum is nearby.

I am going to call it the Westchester Hall of Legacy if that sounds OK?

Totally different subject - are there any stories of earlier incarnations of the Hawks than as Prince Khufu and priestess Chay-Ara in Egypt? Was that their first incarnation?

(oops, I see in one place that it was exposure to Nth Metal that gave them the ability to reincarnate...)

Well, if that is the case, I probably have to rewrite the Legion of Justice story, which specifically refers to several different reincarnations. I hope multiple reincarnations is NOT just Post-Crisis!!

Whether they did or didn't have other lives between Khufu's time and 1939 the Pre-Crisis stories told seem to imply that remembering the past lives wasn't the way it was Post-Hawkworld.  Carter lived his life with no idea he's ever been Khufu until that knife crossed his path and Shiera only remembered the life after meeting Carter.

So I'd assume if they had lives in-between there is nothing to say they were heroic.  Carter could have lived as a serf in the Middle Ages who never left the land he was born on (and never realized anything about Egypt). Shiera could have been a woman who died during from the Black Death at age 11.  Not saying anyone wants to read or write whole stories about this type of thing, just that we also don't need to try creating a whole legacy of heroes that were all Hankman or Hawkwoman during an earlier incarnation. 

Nor do we need to imply that every prior incarnation had Carter and Shiera as lovers.  He could have been that serf in France in 1224 while she was incarnated in what would one day be America. Or one of them could have been incarnated in the 10th century while the other was not reborn during that century at all.

And as for the Legion of Justice- it could be that after they were Hawkman and Hawkwoman later incarnations were actually looked for (especially by other JSA descendants) so there are better records and/or things like the knife (or the Hawk-gear) being used to bring back memories

In the Pre-Crisis Earth-2, there was no "Chay-Ara" -- that is a Post-Crisis invention. She was Princess Shiera in ancient Egypt. Roy Thomas even came up with a historically accurate explanation why Prince Khufu was blonde.

I would like to have Carter and Shiera carry modern versions of maces and flails and other ancient weapons. After all, if you took an ancient mace to Superman, you would end up at least damaging and perhaps destroying an irreplaceable ancient artifact, and they have too much respect, as museum curators, to just wreck valuable museum exhibits.

Does it seem unlikely that somewhere in the JSA brownstone, perhaps in a sub-basement constructed with the super powers of some of the members, that there might be machine shops and forges where they might have been able to create maces and flails and swords using titanium and stainless steel instead of cast iron? And while they were at it, might they have asked one of their magic-using colleagues to enchant these modern replicas to be more damage resistant and also lighter and easier to wield?

Obviously with JSA priority they could have had these things built for them at some other large forging operation where they work titanium all the time, but I think Carter, at least, would prefer the personal touch of making them himself.