So yours still has a problem? Planning to deal with it one day or just living with it? I think I need something that will stick to it to get fed through the sheath. Apparently Anti seize isn't good enough.
I usually clean the cable and the sheath as well as possible of the old grease first. WD-40 actually does work pretty good for this but kerosene or Varsol is even better. Once clean I coat the cable really well with moly grease and reinstall. I do not use Lithium grease because it dries out although it would probably take a considerable amount of time.
Have no idea what the speedo cable looks like...but I bet this would work. Hit a bike shop and pick up a cable luber for like $10 and a can of cable lube for like $5. The cable luber makes life so easy...basically fits around the end of the 'sheath' let the actual cable stick out the end of the tool...tighten her down to create a seal, put the lube straw into the hole on the side and spray away till you see it coming out the other end.