A properly rebuilt and installed tranny should have absolutely zero problems with a long trip. You should have many, many thousands of trouble free miles ahead. As a matter of fact, a long trip maintaining relatively constant speed is the easiest thing you can do to a tranny.
Varying speeds to properly break in mechanical things is an old custom that relates to engines. Engines have piston rings that slide up and down the cylinders, and the surfaces of the cylinders are specially prepared with controlled scratching (called “honing”) to allow proper intial wear by the rings to maintain a miniscule level of oil after the wiper rings go by to provide lubrication for the compression rings, which will be pushing against the cylinder walls. Avoiding beating on an engine was to allow that proper initial wear.
Additionally, the piston rings vary in their travel based on engine speed, and there was a concern that pistons always stopping at the same spot would create a “shelf” at the top of the cylinder that would interfere with their travel when you then ran the engine to higher speeds. Engines do, in fact, develop “shelves” over the miles that need to be reamed out to remove the piston/ring/connecting rod assemblages, but I don’t know that such a shelf developed in the first 1000 miles. OK4450 or one of the others here could probably clarify that.
Trannys have no pistons, rings, or honed cylinders. Automatic trannys have only hydraulic solenoids, gears, and frictional “bands”. They can’t wear in a destructive pattern the way cylinders might. The attached document might be a bit “deep”, but it shows that trannys don’t have the “rubbing up against” wear issues that engine cylinders have.