1. Though the baby was left alone, she didn't cry.
2. Being left alone, the baby didn't cry.
3. Left alone, the baby didn't cry.
(Are the three sentences all grammatical?)
4. Although he had been very tired, he couldn't quit the job.
5. Having been very tired, he couldn't quit the job.
6. Very tired, he couldn't quit the job.
(Are the three sentences all grammatical?)
7. Though it was written in 1900, his novel is very modern.
8. Though having been written in 1900, his novel is very modern.
9. Though written in 1900, his novel is very modern.
(Are the three sentences all grammatical?)
2 and 3, even though they're awkward, mean about the same as 1, yes.
5 and 6 don't convey the idea of "Although" in 4, so they do not mean the same thing.
7 is fine.
8 is very awkward and wouldn't be used.
9 is okay.