extend height of wooden railing
Although it is a nuisance to remove all those banisters, it might be feasible to add a similar number of them. 

Install new banisters between the old ones, but extending upward 25% to 50% longer. Connect their tops with a railing similar to the existing one. 



In this picture, I haven't yet installed the new top railing, but you get the idea. 

The banister spacing is now safer for toddlers, pets, and large heavy toys, and you can select the length of the new banisters to have your top railing at practically any height.