Can a message be encrypted with BOTH mono-alpha and poly-alpha ciphers? For my class assignment, I was given this text;


  Qpuvu vo vv stazpuykzh Hhycmlmv asb. Ad dhyaqva wh uyo uzb jpwww Avlw.
  Tkpjllfdmbp zoatz vzjavfvna ZLHqh. Amva luy yyvlz yu bhk zua zlhvvalaz
  yow llh uldu llzy yzlvao. Hzk caslyv kfzounf zayy sh pvsv. Uopz ala
  yrvhbhm tk ppp Thlll jya. Blz o bblw tol Lsjay hba ljw oro lp nta
  avlnktn.


There is more than one cipher method used, with one of their keys being 'ANNIE'

POSSIBLE METHODS: Caesar, Vigenère, One-Time Pad, Columnar Transposition, Railfence Transposition...

Using Cryptool 1 to analyze the histogram, I figured out that there's a Caesar shift 7 cipher, which decodes the text to:


  Jinon oh oo lmtsinrdsa Aarvfefo tlu. Tw wartjot pa nrh nsu cippp Toep.
  Mdiceeywfui shtms osctoyogt SEAja. Tfot enr rroes rn uad snt seaootets
  rhp eea newn eesr rseoth. Asd vtlero dyshngy strr la iolo. Nhis tet
  rkoauaf md iii Maeee crt. Ues h uuep mhe Elctr aut ecp hkh ei gmt
  toegdmg.


I figured out the plaintext by using columnar transposition through a website. 


  jamesisanundercoverinterpolcophereportstoouroldenemysuptshamshuddinusingencryptedsmsestheyareawareofallouractivitesforthelastfourmonthsthepolicesuspectthatweknowtheyareworkingtogetjamesoutsetatrapforjamesandgetridofhimtonight


Is there a way I can explain why it couldn't have been Vigenère or a one-time pad? Is my assumption that a mono substitution cipher cannot be combined with a poly substitution cipher correct?
I'm assuming that your Columnar Transposition Cipher (CTC) is as described as this site, since I found that the keyword ANNIE works.

OTP

First of all, the combined cipher (Caesar shift 7 plus CTC) can always be the OTP, as long as we don't require a truly random OTP. The simple reason; x-or the plaintext and ciphertext get the OTP keystream.

This is your OTP key;


  zpgzmdgvimgddgwmfdypurgdaagcgqhhulnohospvisfikencaiuspaplrpvdszgpjctgigfzmlrtuordrxzuzttzyllcyuvcdmzbsvnorznadqieerdcneslflvnqztpknyohgagorodtazczrdypyshyrolzigrnvtxaceufmrjusmyvtichxpdxsttpsousllyccusveqhodrnpfzrzuubmtjyvqag


And if you asked if OTP can replace the CTC, the answer yes again with the key;


  sizsfwzobfzwwzpfywrinkzwttzvzjaaneghahlioblybdxgvtbnlitiekiowlszicvmzbzysfekmnhkwkqsnsmmsreevrnovwfsuloghksgtwjbxxkwvgxleyeogjsmidgrhaztzhkhwmtsvskwrirlarkhesbzkgomqtvxnyfkcnlfrombvaqiwqlmmilhnleervvnloxjahwkgiysksnnufmcrojtz


Vigenère

In the Vigenère cipher, the password only affects $\operatorname{StrLen}(\text{password})$ characters whereas the CTC distributes the plaintexts implies they are not equal ciphers.

Note: If Vigenère is equal to CTC then the security will be the same as CTC.

Note: there may be a collision that is for some plaintexts a Vigenère Cipher will produce the same ciphertext as a CTC. This will have very low probability, and generating one is an interesting question.