Simply aim for the right side of the lane ring before you dock, it usualy gets stuck when it shifts towards the left, so this way if it does shift, it'l work.
Or just use /stuck when it stops. Helped me. Or F4 on npcs.
Sindromes is right about it aiming for the left of the mark. It doesn't happen all the time though for some reason (to me that is). Coming into a TL or JG you must swing out wide and try to come in as squarely as possible.
As for docking on bases, it's generally best to use the speed dock facility. Get to know your bases.
Slave liners that use TL's and JG's?
I use them all the time because I don't smuggle....much.
I'm afraid that with that particular beast, it's a matter of learning how to fly the thing.
One other point, try to keep out of 'roid fields. It can take you half an hour to traverse Omega 5, and thats without interjection from those lovely boys in the OPG.
If we do edit the Slave Liner, could it please be renamed/re-infocarded? It's pretty annoying when half the people I meet see my ship and ask why I'm not hauling slaves.