***** NOT A TEACHER *****
Hello, Diamondcutter:
I do not claim to have the answer, but I have found some information that may interest you.
1. "Rather nervous, the man opened the letter."
2. "The man, rather nervous, opened the letter."
3. "The man opened the letter, rather nervous."
"Rather nervous" is a supplementive adjective clause.
4. "Being too nervous to reply, he stared at the floor."
5. "Too nervous to reply, he stared at the floor."
The book says that #5 is a shorter way to say #4.
And -- if I understand the book -- #4 is a shorter way to say something like: "Because / since / as he was too nervous to reply, he stared at the floor."
James
Source: A Comprehensive Grammar of the English Language (1985 edition) by Professor Quirk and three colleagues. Pages 425 and 996.