What is the etymology of the 하십시오체 sentence endings?
Some conjecture on my part: The spelling of the indicative and interrogative endings makes me think that 습 and 니다/니까 were once separate, because the ㅂ is never actually pronounced as ㅂ. But it might have been just a choice made when the orthography was standardised.
Your intuition is along the right track. The spelling of Middle Korean is well documented, and it was evidently a much more agglutinative language: in summary, it is descended from the Middle Korean -ᅀᆞᇦᄂᆞᅌᅵ- (Yale: -zopno.ngi-)
In Middle Korean, as well as the "slot" of subject/addressee honorification 시 (which hasn't changed much since), there is also a "slot" for object exaltation / honorification. This function was lost from the verbal morphology from the 17th century onwards, but before then it was the archaic hangeul syllable ᄉᆞᆸ (Yale: sop). The ㅅ could assimilate to ㅿ (Yale: z) after nasals, liquids or vowels; or ㅈ (Yale: c) after t, c or ch. The final ㅂ could also become ㅸ (Yale: W), making the morpheme ᅀᆞᇦ (Yale: zoW) in intervocalic position.
As ㅿ would later disappear across the language, as well as the arae a ㆍ after vowels, that left just the ㅂ portion in Modern Korean to represent this portion in verbs with stems ending in vowels or in ㄹ. As its function as object honorific had also reduced greatly, it just simply became part of the "하십시오체/합쇼체" speech level.
In (non-liquid) consonant stems, the ㅈ became ㅅ in this context, and the arae a ended up as the vowel ᅳ in such closed syllables, so that ᄉᆞᆸ became 습.
The second part was the continuative marker / processive marker -ᄂᆞ- (Yale: -no-), which reduced heavily across a lot of verbal endings. It ended up coalescing into the next morpheme in "하십시오체/합쇼체", but remained its own syllable in "하소서체", with its arae a becoming ᅡ instead.
Next is the polite style marker for Middle Korean: ᅌᅵ (Yale: ngi) [note that this is not 이]. This velar nasal seems to have had very marginal position in native Korean words, and in this case appears to have changed to ㄴ while nasalising the preceding consonant. Most instances of ᅌ were resyllabified, making it the final ㅇ of a previous syllable [compare how 가히 kahi + ᅌᅡ지 ngaci became 강아지 (Yale: kangaci; RR: gang-aji)].
These three syllables were pretty much completely independent in Middle Korean, and the polite style was used quite frequently, even without object honorification:
그딋 ᄯᆞᄅᆞᆯ 맛고져 ᄒᆞ더ᅌᅵ다
kutuys stolol maskwocye hote-ngita
(He) has been wanting to meet your daughter
The -다 and -까 endings are derived directly from Middle Korean -다 and -ᆺ가 for declarative and interrogative sentences directly (although there were other endings that have become archaic in 21st-century Modern Korean).
The imperative ending -읍시오 was on the other hand not descended from Middle Korean, which preferred using -쇼셔 instead (which exhibited vowel harmony), although it bears resemblance to the 하소서체 speech level of Modern Korean. Instead, late 17th century Korean developed -소 as its main imperative, and it received an "upgrade" to modern "하십시오체/합쇼체".
I am not an expert, but I will just leave here what I have found.
For 겸양법 (Some people call it "object honorification," but I am not sure whether it is a proper translation), Middle Korean had these three characters that were attached to verb stems when the endings started with a consonant (ㅂ became ㅸ when the endings started with a vowel):
ᄉᆞᆸ (when the stems end with ㄱ, ㅂ, ㅅ, ㅀ, or ㅎ)
ᅀᆞᆸ (when the stems end with a vowel, or ㄴ, ㄹ, or ㅁ)
ᄌᆞᆸ (when the stems end with ㄷ, ㄵ, ㅈ, or ㅊ)
According to 백문식 who wrote an etymology dictionary, those pre-endings (-ᄉᆞᆸ-, etc.) came from the verb 
다. meant 白 (to mention, to state, etc.).
At that time, the pre-ending -ᅌᅵ- was used for 공손법 (They call it "addressee honorification"). For example, 먹ᄂᆞ니ᅌᅵ다 is now interpreted as 먹습니다. Some characters including ㅿ, ᅌ, and ㆍ disappeared (ㅿ and ᅌ disappeared earlier than ㆍ) and honorification changed over time, which affected the characters I have just mentioned and the following happened:
-ᄉᆞᆸᄂᆞᅌᅵ다 ＞ -ᄉᆞᆸᄂᆡ다 ＞ -ᄉᆞᆸ늬다 ＞ -습니다
but, in consideration of several entries and example sentences in a dictionary, I can supplement the history with the following:
-ᄉᆞᆸ- + -ᄂᆞ이다 → -ᄉᆞᆸᄂᆞ이다/ᄉᆞᆸ노이다 ＞＞ -습니다 (used after a consonant but not after ㄹ, ㅆ, or ㅄ) (1933) ＞ -습니다 (used after a consonant but not after ㄹ) (since 1989)
-습니다 is used for the "addressee honorification" not for the "object honorification." This shows a change in honorification.
The history of -습니까 can be said as the following:
-ᄉᆞᆸ- + -닛가 ＞ -삽닛가/습닛가 (1934) ＞ -습니까 (since 1957)
-ᄂᆞ니잇가/ᄂᆞ닛가 (after a stem) and -니잇가/닛가 (after a stem or a pre-ending) were used to form "yes or no" questions. -습니까 can be used with or without interrogatives. It is quite natural that ㅅㄱ or ㅺ became ㄲ; for example, 아까 was once written as 앗가.
As for -읍시오, some believe that, after -ㅂ시다/읍시다 had been formed, -다 of -읍시다 got replaced with -오 to form imperative sentences.
-(ᄋᆞᆸ)사ᅌᅵ다 ＞ -(ᄋᆞᆸ)새이다 ＞ -ㅂ새다/ㅂ세다 ＞ -ᄇ시다 ＞ -읍시다
-읍시- + -오 → -읍시오
Nonetheless, it does not explain why -습시오 does not exist (-ᄉᆞᆸ시- existed before).
김현주 claims that people who were not well-versed in the court language used -ᄋᆞᆸ시- for the "addressee honorification" when the subject of a sentence was equal to the addressee. It seems that the author believes the following:
-ᄉᆞᆸ- + -으시- → -ᄋᆞᆸ시-
According to the dissertation, such an unordinary combination became possible when -ᄉᆞᆸ- became used for the "addressee honorification" because -으시- was (and is) used for 존경법 ("subject honorification"). If this is the case, the absence of -습시오 is quite understandable.
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