Lots of us are hypermobile, and some hypermobile people have joint pains. What should they do about it? There haven't been many trials. One trial in children (see here) showed no difference between generalised and targeted physiotherapy. One study looked at whether it is better to exercise the knee to a normal straight position or to exercise it into the hypermobile, overextended position. They found that kids were happier when being allowed to extend into their 'hypermobile range', but that parents thought their kids were doing better when they were restricted to the 'neutral position'. Go figure!
Bottom line.. no evidence for any particular type of physiotherapy, but exercise does seem to help! Keep those muscles strong!