if you can, I'd recommend cutting a spiral groove through the exit hole and a pinhole at the top(to equalize with atmospheric pressure) as the act of sealing the STP against your skin creates a vacuum that reduces the exit flowrate from the STP
if the fluid in the basin can exit in the same fashion like emptying a bottle by swirling it, then the flowrate should be high enough that the basin doesn't have a chance to overflow
not sure if this is the best method, just one that I think has the best chance of working, although someone might have a better ideaπ€