Well, I don't mean literally meandering
, mainly finding a sorta-parallel route through neighborhoods without having to use Hall. Something like (and take this with a big grain of salt, as I haven't lived in Beaverton in about 10 years, and I don't know how bike-suitable some roads are in that end of town - I lived on the north end)
Broadway & Watson - to Lombard
South on Lombard to Denney, jog over to Anne, then Hillcrest.
Pop out at Ridgecrest, ride along the sidewalk to Greenway, cross Hall at the signal on the south side of Greenway (avoiding the obvious right hook by people barreling down the hill at 40mph). Still a little sketchy past the driveway at Albertsons, tho'.
Ride through Greenway Park, cross under Scholls, as far south as you can go (can you get out at Dakota? This is where my knowledge of the park is really fuzzy). You might get forced off around Black Diamond, I can't remember.
South of Dakota there should be a trail near the tracks that goes to Tigard. Take Tigard across under 99 into downtown. Yeah, it's downtown but at least everybody's moving at a crawl, right?
From downtown, take Commercial or Burnham (dunno which is better, honestly) to Hall. Depends where your destination is.
You could start on the west side of Hall (like Erickson or Main - but that's a lot of stop signs through Beaverton) but there's no good way past Hart w/o taking Sorrento, and while it's less traffic than Hall, there's a lot of momentum coming down the hill that puts you at risk if somebody pulls out in front of you. You could meander further west by Highland Park, but I was trying to keep you near your original route. As I kid I remember some trails cutting from Beaverton High towards Hyland Forest, but I don't know if they even exist anymore.