Discharge ambassador overcome by the hard stuff (5)

I believe the answer is:
rheum
'discharge' is the definition.
(I've seen this before)
'ambassador overcome by the hard stuff' is the wordplay.
'ambassador' becomes 'HE' (His or Her Excellency).
'overcome by' indicates putting letters inside.
'the hard stuff' becomes 'rum' (I am not sure about this - if you are sure you should believe this answer much more).
'he' inserted into 'rum' is 'RHEUM'.
Can you help me to learn more?
(Other definitions for rheum that I've seen before include "Watery discharge; sounds like space" , "Rhubarb genus; a head cold" , "Poetic tears" , "nasal discharge" , "drips from the nose" .)
