Here's something to try - make your own film dryer out of a hair dryer and a tube of some fairly heat resistant material (you also might think about putting an air filter in front of the blower end). I can't remember the name of this old product but a lot of traditional labs had them, it was basically a big heating element with a fan, and a tube the right size to hold film reels with a metal clip at the bottom to hold them in. It actually looked like an over-sized hairdryer, mounted on the wall, and would dry film in about 10 minutes. I know they stopped making the real thing about ten or fifteen years ago but I don't see why someone couldn't build one at home.
A more dust-prone method is just to turn on the hair dryer and close the bathroom door...
About lines falling down with film still attached - get a metal clothes hanger, turn the hook 90 degrees, hang it from the shower curtain rod, and clip your film onto the bottom of the hanger. Works for me!