Sounds like a sensible idea to have stopped the combined pill. I'm not so sure about you never being allowed to use it again- you can take it with a history of migraines, it is only focal migraines (where you get neurological symptoms such as weakness, numbness of tingling) which are a complete no-no. However, it would be a brave doctor to suggest that you restart it and prescribe it again!
The POP seems a sensible choice. Which one have you been prescribed? You are right about the unpredictability of periods. Some women will be lucky and get nothing or the occasional day of spotting, some will have regular cycles, some will get lots of infrequent bleeding. It doesn't tend to make your bleeding any heavier than usual. You won't know which you will be until you have tried it I'm afraid.
The POP is a relatively low dose of progestogen, but it can increase your appetite slightly and a few women put on weight. In my experience, this isn't a common problem with any method except for depo injections.
Headaches can get worse with the POP, but from what you say I wouldn't expect them to. It sounds as though it was the oestrogen in the COCP causing your migraines to worsen.
The mefenamic acid won't mess up your cycle or screw anything up as its just an anti-inflammatory painkiller. There are no hormones in it. It can make bleeding lighter, but it is usually prescribed for the analgesic effect. Don't take ibuprofen with it too.
In the long-term, if you try the POP and get on OK with it then you could continue with that (even up to the menopause if you want). The other option would be a long-term reversible method that is progestogen-based such as the injection (I personally don't like this but it is good a stopping periods), an implant (fab) or a hormone coil (Mirena, which is licence specifically for controlling heavy bleeding as well as contraception).
I'll stop being dull now!