As a native Japanese speaker, let me answer. I am really afraid to say, do not misunderstand the "structure" of my tongue, otherwise you will probably misunderstand forever.
First off, the sentence you made perfectly makes sense.
Now let me explain "linguistically"
”してたの” will be divided into, well, 4 pieces! ( What a complex language, my friend, but the
since the structure is completely different from English from the very basic, please hang on to it )
First し is variable form of "old" word "す”, which according to the word that come after
it changed to "し” ( linguistically categorized as "conjunctive form" ( = in order to continue to next word て )) ---> in English, meaning "do"
Second "て” was actually, or historically, a verb, however, it lost the original meaning and
currently categorized as noun so that the sentence can be continued. ---> In English, meaning, nothing, just a "superficial" noun.
Third "た” means in English, "finish", being categorized as "auxiliary".
Finally, "の” is expressing the "question" in English, so to say, linguistically categorized as a particle.
Soooooooooo, after long jargon, "してたの” means in English, "( you ) did so?"
Since Japanese is S-O-V, you have put in "熟睡” correctly. Because it is a noun = O.
I explained V in your sentence above.
熟睡＝O + してたの = V = "did you so?"
Wow, I think I am going nuts. ha-ha.