We have a similar situation, although maybe not as obvious. Our long hall (roughly 12') is narrow and then it angles off to the left to the laundry room. Laminate in all this area. We ran the laminate lengthwise down the hall and crosswise in the short hall and laundry. From there it goes to the door to the garage. It looks fine!
The short section of hall and the laundry are not guest areas, so we are the only ones who see it.
Pergo and Quick Step say 3/16" in 6' is the allowable dip. I can't imagine that 3/8" would be allowable; the joints would crack.