Kesha is now a US Citizen! 
The whole applying for a Consular Report of Birth Abroad turned out easier than I thought it was going to be, and our experience with the US Consulate here was actually quite positive!
We followed the instructions online, and they were fairly accurate. Here are the items the consulate asks for:
Fee: The cost of the application for the Consular Report of Birth Abroad is USD $100.  This  fee is non-refundable, and will not be returned if it is determined  that citizenship was not transmitted to the child at birth.
Child's birth certificate:  You must submit a certified copy of the child's birth certificate issued by the Ecuadorian Civil Registry.  The Ecuadorian Civil Registry may provide different versions of this document.  Please make sure you request a direct copy from their Book of Records.  Other versions will not be accepted. (Note: this is the handwritten copy, not the printed copy. They will not accept the printed copy) 
Proof of parents' identity:  Each  parent must submit an original or copy of a government-issued photo ID,  such as a driver's license or Ecuadorian cédula, or the photo page of  his/her passport.
 Pregnancy Records: For example, echo sonograms, doctor's certificates, hospital bills, and photographs of mother during pregnancy.  (Kindly  refrain from bringing used pregnancy tests, blood samples, umbilical  cords, or other items that may be considered a biohazard.) (Note: I was asked to send additional ultrasound pictures, so bring a few with you when you go) 
Record of Physical Presence of U.S. Citizen Parent in the United States:  This  supplemental form is to be filled out by the U.S. citizen parent,  detailing all periods of physical presence in the United States.  This form must be signed and dated by the U.S. citizen parent. (We did not fill out this form and they did not ask for it. There is something similar on the actual application)  
Documentary Evidence of Physical Presence:  In  cases in which only one parent is a U.S. citizen, that parent must  submit evidence that s/he was present in the United States for the  required amount of time prior to the birth of the child in order to  transmit citizenship.  Such evidence frequently  takes the form of school transcripts; tax records, including 1040 tax  returns or W-2 forms; pay statements or other evidence of employment;  annual Social Security statements; photos; apartment leases; or other  evidence.  These are merely suggestions, and you are encouraged to submit all available documentary proof.  If  no such evidence is available, the consular officer will advise you at  the time of your application what alternatives you may have for proving  your presence in the United States. (The  first lady told us we needed proof of 5 years in the US, the second  said we didn't, so we didn't have to send additional proof... I think it ended being that we didn't need proof because we are both citizens) 
For Parents Who Were Married at the Time of Birth of the Child:
Proof of parents' marriage and termination of previous marriages:  If  the child's parents were married at the time of birth, the consular  officer will need a certified copy of their marriage certificate.  If  either parent has been married previously, the consular officer will  request evidence that any previous marriages were terminated, such as a  certified divorce decree or death certificate. While these documents are  not always required, it is to your advantage to bring them in case the  consular officer requests them. (If you were married in Ecuador, this is also the handwritten form, not the printed one) 
In addition to the documentation described above, the Consular Officer may request the following: 
Proof of Paternity/MaternityRegardless of the marital status of the parents, in  cases in which paternity or maternity is in question, the consular  officer may request additional evidence of the biological relationship  between the parents and the child.  Sometimes this  proof may take the form of family photographs, baptism records, or  other documents. In other cases, DNA testing may be suggested.  If  DNA testing is appropriate in your case, the consular officer will  advise you about the process. Please note that DNA testing will not be  accepted if it does not meet the guidelines explained by the consular  officer. (Didn't apply to us)
Additional EvidenceThe  consular officer, at his/her discretion, may request additional  documents or other evidence as necessary. You will be advised at the  time of application if such evidence is required in your case. (We were asked for a hospital bill from Kesha's birth, but that's it.)
The cost was $100 and we paid cash on site.
We also applied for Kesha's passport at the same time. You simply need the passport application and 2 2"x2" photos, plus $105, and you're set.
We were also able to pay cash on site for her passport.
When you are approved the give you instructions to go to the DHL office and prepay for your documents to be sent to you. This cost $9 and was extremely easy to take care of.
All in all a very easy process. Our missing documentation is being sent via email (much easier than driving it back to Guayaquil!), and her certificate of birth abroad and passport will be sent via DHL right to our house!
I'm glad that's over and done with! Now we're just waiting on my Ecuadorian citizenship to be approved.