I've never fixed one like yours- they have all been in a circular manifold- but the same principle would apply, that gel strip manifold- turns to mush and leaks after about 20 yrs- so yes, the box would need to be opened (removing it is easiest) and lines plugged into the individual solenoids and routed out (through a cut hole) and spliced to the colored lines- completely bypassing the manifold.
You would have to study it first- but if holding the line to one side works, maybe you can try to seal the leak first, or tie it back in that position- may last for a week or maybe a couple yrs, who knows.