I’ve been trying to recite Ziyarah Ashura every night but I recite the Laan and Salam just once instead of 100 times due to time.

Does this still count as reciting Ziyarah Ashura or is it invalid since I fall short in reciting all of it?

Yes it does count. Now if you recite those 100 times it will have a greater effect, but even it you don’t, it still counts.