I think the things to consider here can be broken down into three questions. Question one might be , when gold coins were in circulation (pre-1933), did common people actually carry them and use them to pay the bills? A second question might be, what denomination gold coin would most likely be lost? A third question then would be, Where is the most likely place to look?
In my opinion I think the answer to question one is that in the early years, 1849 to maybe 1880, a $1 gold coin was not considered unique by the general population and that it would be used like any other coin ($1 gold coin minted 1849-1889). It would not be put in a fruit jar and buried in the back yard. My research indicates there were more gold coins in circulation in the 1850's than silver dollars. (See my other post, gold $1, O-1849 250,000 minted). You might be interested in the fact that the L&N railroad operating in this area paid their workers in $5 gold coins up until some time early 1900's. I'm sure those workers paid their bills with those gold coins. The L&N probably wanted to show the area what good they were doing for the local economy.
My answer to the second question would be, in its time frame of common usage (1849-1889), the $1 gold coin due to its low value and really small size, would be the one. Maybe the 2.50 gold. The $5 way too big and valuable for its time, not to be searched for if dropped. Larger denominations - out of the question, because of their high dollar value. I think they did go into the fruit jar and then turned over in 1933. However it is estimated that only 20% of existing gold coinage was turned in.
Question three - I wish I knew. But consider this fact, the 1849 gold $1 found in St Louis was NOT a New Orleans minted coin. That still leaves 250,000 1849-O's still unaccounted for.
looking for the gold Oh yeah.