Why do we omit "as" when reducing the subordinate clause of this sentence? Sentence: As I had slept for ten hours, I felt marvelous. With reduced clause: Having slept for ten hours, I felt marvelous.

When we write, "As I had slept for 10 hours, I felt marvelous" we are using a descriptive phrase ("As I had slept for 10 hours") with a main clause ("I felt marvelous"). When we replace "as I had slept for 10 hours" with "having slept for 10 hours," we are transforming the sentence to be even more syntactic. Syntaxis is the use of subordinate clauses, while its opposite, parataxis, is the use of clauses next to one another without subordinating pronouns. An example of parataxis in this sentence would be, "I slept for 10 hours, and I felt marvelous."
Here, the descriptive phrase "as I had slept for 10 hours" is replaced by a participial phrase, "having slept for 10 hours." This is acceptable (even preferable), because the past participle, "having slept" shares its subject with the main clause, "I." Participle phrases, which can be present ("sleeping") or past ("having slept"), are a bit more precise because they share a subject with the main clause. If this were not the case, as in the sentence, "as it was raining, I couldn't go to the beach," such a substitution would not be possible.
So, we omit the conjunction "as" because the participle ("having slept") is explanatory in nature.