The film isn't particularly more susceptible to scratches in the camera than otherwise, but the felt light trap on 35 mm cartridges, and the round trip the film makes out of the cartridge and back in offer more chances for scratches to occur. It sounds like most of your scratch problem is in general handling, one way to eliminate the camera as a possiblity would be to get a roll from the 35 commercially processed. If the results are similar to what you've encountered with the 120, then you know it's your developing/printing procedure.
The anti-halation is a dye that washes out in the pre-soak, or the developer. It never ends up as stringy gunk. If you are using Photo-flo pre-mixed (the best way, IMO) and re-using it (not necessarily so good) it might be growing things, mix some fresh. Or you might have other chemistry growing things. I would start off with making new batch of all chemistry, with a thorough cleaning or replacement of the bottles.
What color is the stringy gunk?
Finally, the brand of film makes a difference, Ilford, Kodak and Fuji are the best at resisting scratches.
Other things to consider, do you wipe or squeege the wet film? Is your water filtered?