As I understand it, lesions themselves are painless, so the pain you are experiencing is not coming from the lesions, but from the interference they are causing to your body’s communication systems.
The resulting garbled messages can get interpreted as “pain”, even though when there is no physical cause. That doesn’t mean the pain is imaginary: the pain signals are real, but caused by a “miscommunication”, not genuine injury.
Alternatively, the lesions can also interfere with motor communications (movement), which could mean, over a period of time, that your muscles are becoming weaker, or your gait and balance are a bit “off”. These things, in turn, could be an ACTUAL source of pain - e.g. if you’re constantly putting more weight on one leg than the other, this is eventually going to set you up for aches and pains.
Personally, I think “generalised” pain is a very common problem with MS, and that your 30% figure is rather on the low side.
Effective treatment of pain requires first identifying what caused it; i.e. is it garbled messages being interpreted as pain, or is it real physical pain, caused by muscle weakness or abnormal gait, for example?
The approach in each case is different. If it’s the first type, it will ONLY respond to drugs specifically prescribed for nerve pain, not conventional painkillers like cocodamol.
If it’s the second type, it may respond to conventional painkillers, but you may have to experiment with both type and dosage to get the best results. There are alternatives to cocodamol available on prescription, if you find this isn’t working for you.
Physiotherapy can also help with pain that is caused by physical changes to muscle strength and the way you walk - you can do exercises to improve strength and balance, which may reduce pain.
Finally, even though it’s not a painkiller, I wonder if you are already on a muscle-relaxant such as Baclofen? Sometimes the pain is caused by excessive resting muscle tension (aka spasticity), because instructions to tell your muscles to relax aren’t getting through properly.
This understandably makes the muscles feel tired and crampy. So sometimes, if you take something that forces them to relax, you will find the pain eases too.