Currently moving on a ladder with Up/Right or Up/Left or Down/Right and Down/Left halt the character from moving.
Although this could be by game design, it is very unforgiving on the controls.
I would suggest the character to keep moving towards the direction pressed and as soon as they reach a platform that allows left/right to continue to the platform.. in other words there should be no halting on movement while more than one directions are performed on the controller.
For example, Down-Right on a ladder should move character down until they reach a platform level and then the character should move off the ladder (even if the ladder continues) and move right on the platform.. while on the platform and still holding Down-Right, they should keep moving right until they reach a ladder and then climb down.
You followed a similar logic with Donkey Kong, and it works perfectly!
EDIT: I tried a version on MAME and it does halt movement with 2 inputs. So this request is probably a feature improvement.
My experience was more with the Intellivision version which does slide/keep moving
BUG: I noticed on your version walking up and down ladders is a bit off-centered, and can also climb a pixel up/down while near a ladder and not entirely centered on it.