I feel for the OP because work dumps are never pleasant especially if you only have one trap!!
A place I worked at previously had only three traps and went through a lot of traffic and there was one deviant that used to fuse his muck to the porcelain. God knows how, it seemed to actually alter the chemical compostion of the Armitage Shanks….
Back to the OP – Personally I would embrace the situation and go for the manly approach, make as many neanderthal style grunts as possible, take as long as is practical and then emerge triumphantly fist pumping the air singing “I’m walking in the air.”
You will become an office legend.