>>So is there any ethical way for me to approach the institution? Do I
offer five times its market value or only double.  Money has to come into
it at some point.

Just ask them if they're willing to sell. The answer will be yes or no.
Thirty years ago, when my wife was pregnant, I found a clutch of cradles in a
local museum and asked if they'd consider parting with one -- specificially,
this one. They thought it over, discussed it, and came up with a price that
was very reasonable.

And I'd rather see this piece in your home than in some museum basement!!
       Jay Fahey