There are two ways I can think of to get rid of the remaining water:
As per LDC3's answer, flush the system with ethanol which will hopefully not have the problem of slow dry time.
As per LDC3's answer, flush the system with ethanol which will hopefully not have the problem of slow dry time.Put the glassware in an oven, which will also nicely sterilize the system.
Put the glassware in an oven, which will also nicely sterilize the system.