I'm in a similar situation... my Bassoon was stenciled "Imported by H.N. White, Cleveland" which later got merged into King iirc. As far as I know it was made in Germany or Czechoslovakia between 1918 and 1965.
Not a bad bassoon after it had a decent overhaul (including fixing naughty boreworm holes) but I'm not sure if it is the same brand they used later on.
I also bought this on ebay, it's a risky thing really. Can be good and bad.
Unless it is expressly stated that it has been recently serviced and is ready to play expect to spend some money
at a reputable woodwind shop to get it properly adjusted.
I also have some old sad lesher bassoon still in a box which I will use to practice repadding and such... it's not quite up to the quality of my White
I can't see a King on ebay atm, would you have a link ?
Cheers
James