SuStel:

qen HochHom qep'a'Daq jIjeSbe'pu'.

if this is supposed to mean "recently I didn't participate at the
greater part of the qep'a'", shouldn't it be {qen qep'a' HochHomDaq
jIjeSbe'pu'} ?

No, it means recently I haven't participated at most qep'a'mey.

-- 
SuStel
http://trimboli.name