"Obsequy" as a more concise synonym of "sycophancy"
Solution 1:
An interesting dilemma!
In Middle English, obsequi was firmly aligned with obsequious:
obsequi n. (1) also obseque. [L obsequium]
Obedient service; the dutiful performance of a certain duty; also, the attentive service of menials
But it was still used in the singular form to refer to the funeral ritual:
(a) a service for the dead; funeral
Although servile insincere flattery was probably among the certain duties in the attentive service of menials in that day, the word is no longer used that way. The vestiges of obsequy are only preserved through the corruption of exsequiae: religious rituals. To use obsequy as a synonym for sycophancy would require turning the clock back quite a few hundred years.
Descriptively, the dilemma is interesting, but it also simple: not today.
Prescriptively, if you start using obsequy that way, it might not take a lot of effort to resurrect the old meaning. Words never die; they just sleep.
Solution 2:
The OED (Oxford English Dictionary) has obsequy. It is listed twice, the first entry dealing with the meaning concerning funeral rites.
The second entry lists two senses:
a. Ready compliance with the will or pleasure of another, esp. a superior; deferential service; obsequiousness.
b. An act of compliance or deferential service. Freq. in pl.
Several sample extracts are provided for each dating from 1425 to the present time.
It derives from the classical Latin obsequium - compliance. A French version obseque is dated from 1375.