I am trying to modify $node via hook_node_load but I do not have the current node in the list of $nodes handled by hook_node_load when I check it with devel's dpm. I only have some nodes from a node_load_multiple call I make in the module. Should I use hook_node_view instead? But hook_node_view says it can only modify node content.
It depends on when and where you trying to modify the $node. hook_node_load runs every time a node is loaded,whereas hook_node_view runs only when a node is about to be rendered on the page.
The reason you might not be having the node id in question in you hook_node_load may be because the context in which you are calling hook_node_load might be wrong. In order to test you can create a dummy callback and call the node_load() in it with you nid in question. You can see that once you call the node_load() api, it will invoke a call to hook_node_load.