Question: I used to work for a restaurant that had waiter teams. There were three roles: *Aid, Lead, and Follow-up.* 

* The Aid was basically the busboy.
* The Lead greeted the customers, took the drink orders, got the drinks, and took the food orders (most of the time).
* The Aid and Lead were often out of sight to the customers, getting stuff outside the section.
* The Follow-up handled the flow of the service, quality control, customer relations, and getting paid. The Follow-up never left the section, and was usually the most experienced waiter. Described here it sounds stilted, but it wasn't: it worked very well.

I am looking for a word to replace "follow-up" that is more elegant to hear and see, and that reflects the seniority and sophistication of the role.

Answer: 
Absolutely not. Pronunciation never determines spelling in English. Spelling has its own ancient history, one far removed from any attempt to encode pronunciation.

There are all schwas:

* Al**a**n
* mount**ai**n
* kitt**e**n
* cetac**ea**n
* for**ei**gn
* sat**i**n
* atomic**ia**n
* mot**io**n
* lem**o**n
* aut**u**mn
* Er**y**n
* rhyth**m**
* ac**r**e
* litt**l**e

In the case of the two most commonly misspelled words in the English language, *separate* and *occurrence*, these are spelled that way because of how Latin respectively spelled *sēparāre* < *sē* + *parāre* and *occurrencia* < *occurrentia*. 

The same sort of thing is true with a very great many other words in English. You have to understand their history to understand their spelling. Pronunciation is virtually immaterial.
The other answers answer the question I think, but just as regards to "separate", it is possible that people who misspell it aren't predicting an "e" from the schwa sound (after all, Boondoggle's data shows that "o" would make as much if not more sense there as "e" does), but are spelling by analogy with the word/syllable "**per**", which is pronounced with a schwa/r-colored vowel the same way as the "par" in "separate", whereas the word/syllable "**par**" in isolation is not.