In my opinion, only playing rudiments is not the complete answer. The path to a stronger left hand is manifold. Rudiments are the possible combinations of sticking on the drumset, yes. But it's a repetition exercise. What I mean is that you can repeat something for a while with improper technique and be able to play the rudiment perfectly and still have a weaker hand.
A couple of years ago, I switched to a fully ambidextrous drumset (meaning I can lead both as a full lefty or righty). When I did, I noticed a huge difference in the way I held the stick between my right and left hand. The difference was especially apparent when I played doubles. It made sense since playing when we cross hands, we treat both hands differently in most scenarios. So that's the first thing I changed : I played those rudiments while paying attention to the left hand, adjusting my grip and the way I played to mirror my right.
The two most important exercises I used to do to improve (and still do) were quite a bit more simple than rudiments. The first is just playing linear patterns between the hands and the feet (like both hands, both feet, right and left foot, left hand and left foot, etc.). This will practice your stamina which the left side always lack as well as making it a coordination exercise by putting it in relation to your other members. The other exercise is just playing unison of the same combinations. Again, you will notice and feel a HUGE difference between your left side and right side (the left side will start to flam very quickly). Practice at different levels of volume for long periods. And of course, start slow!
The last step is quite dramatic but optional : play left handed a bit! Leading with your left will confuse your brain and again, will make you more aware of what you are doing. It will also train your left hand to move around the drumset. This is important because while rudiments will help you to move your left hand, they are usually done on a single surface (the snare drum) which has a very different feel than other drums or cymbals. By playing on those other surfaces, you will train slightly different groups of muscles (especially in your hand) that aren't as strong as your right. Also, listen carefully to the sound produced by your left hand (and foot).
Needless to say that it is a pretty long journey : most of us start playing cross handed and never really question this way of playing until we are confronted with those problems or situation. And when they happen, we must catch on to all those years of playing that way. But I tell you, after a while, you will feel that much more confident and free in your playing. It's all worth it!
Cheers and good luck!