Since you are greasing, my guess is that the tongue latch is slightly damaged or bent and may need replacing.
99% liklihood that this is your answer. In all my years of towing many things, this is the primary cause for the trailer to not detach easily from the ball.
Also, you're using a 2-5/16" ball, not 2-5/8". If you have a 2-5/8", its because you purposely sought out that size. They are available, but they're not sold at the store (generally custom-made only). I think they use them for mobile homes and similar trailers. And unless you beat your tongue coupler onto the ball with a sledge hammer, you'll never get a 2-5/16" coupler to fit on a 2-5/8" ball.
And no, don't even consider towing on the road with a smaller size ball.