I haven't ever seen an inline adjuster gummed up that badly. What normally makes any cable adjuster hard to turn is the cable outer jamming into the adjuster so that turning the adjuster just twists the cable outer. I add a bit of my universal tool (grease-based chain lube :) to where the outer enters the adjuster and give it a couple of seconds to penetrate before having another go.
What I suggest is taking them off the bike, taking them apart and greasing them. Grease both the threaded part and the cable entry.
In this pic you have the turning part in a shiny silver, and almost hidden inside it is the stationary part that's a darker colour. I would unscrew those parts and grease the thread, then also put grease in the end of the rotating part - into the opening at the bottom of the left hand part above. That way the end of the cable outer that goes into there can slip easily when you turn the silver part.