I have no important advice to give you, but here's what I have. There is a Loretta BODTMANN who posted a query on the OSINSKI board at Ancestry.com. Perhaps you can alert her of your search in case she hears from your uncle in the future. By the way, there is no time period mentioned in your query.
There are three decedents named Anthony BODTMANN on the online Social Security Death Index. I use RootsWeb's version :http://ssdi.rootsweb.com
These men lived 1905-1988, 1922-2001 and 1930-1995. If you know which is the birth father, you can add an annotation to his entry on the SSDI, by clicking "Add Post-em." Your annotation could include your name and permanent address.
I am not optimistic about the chances of a relative seeing your Post-em. First of all, the family genealogist may have checked the SSDI before you posted the Post-em. He or she might consult an online version other than RootsWeb. When he or she consults the SSDI in the future, who knows if RootsWeb or any other host will still have an active website? There might be a merger or reorganization.