Unfortunately it is normal, sorry they haven’t replied, it may be a busy time, but that is always the excuse there. The real issue is the school has just gotten too big over the last few years and trying to reach admissions/financial aid has become a nightmare of no response or incredible hold times on the phone (40 minutes+). It is a huge pet peeve of mine about USC, they are becoming less private like all the time. I get much better response at UCLA and even tiny staffed Cal Poly. Also less pompous attitude and nice people at the other schools. Sad but true. The “you should know you are lucky to be here” attitude shines through way too often imo and is gonna bite them back at some point.
Back to you - yes, send the letter if you think it is needed. Some will say they want to see if you can follow direction and only asked for two, but I believe in your case, it sounds like this information would add great value. They will eventually reply and at that time you can let them know you you felt it important to send and apologize for any inconvenience this may cause - or something similar and polite.