Four-drawer chest... how old?

I hear you but, that is a dicey proposition at best these days with antique furniture. The middle market which is 80% of the total old furniture market is WAY DOWN these days, I don't think there has ever been a better time to buy antique furniture in my lifetime. It is literally cheaper than Ikea sawdust furniture.
Take the above chest you were considering, it's a solid hardwood carcass/drawer fronts with solid white pine secondary.
You can't buy the lumber it would take to build that chest today for $350, never mind the labor to construct it.