A few thoughts:
I use HP5+ quite a bit, in both 120 and 4x5 and have not seen anything like what you are seeing. My 'normal' process is:
I use a Jobo processor, so temperature and agitation are very consistent from one processing session to the next.
I presoak for 1min in tap water.
I mix my developer, stop and fix from liquid, and use distilled water.
After fix, I wash in tap water.
As a final step I let the film soak in a bath of distilled water with a wetting agent (edwal?) and then hang the film from a corner, so that as the water sheets off, it has a corner for that last drop to migrate to.

I do not squeege per-se, but I do gently wipe the roll film between my fingers to get some of the water off.

The negatives usually hang overnight in my (relatively dust free) darkroom.