I was having very heavy, painful periods that were becoming more frequent after having my dd. I had problems with the mini pill, and couldn't take the combined pill because of severe migraines.
I tried Mefenamic acid, and although this slightly reduced the amount of blood I lost, it didn't really help a lot with the pain. This also irritated my stomach, as it is similar to Ibuprofen.
I was then given the same 3 options as the OP... and I was pretty much railroaded into having a Mirena fitted.
2 years on, and the bleeding is almost non-existent. I get some light spotting, mood swings and a few zits, but this is nothing compared to when I couldn't go out because I was so worried that I'd flood, or have such bad cramps that I'd be bent double.
The hormone dose is lower in the Mirena because it is a slow release implant, and is only meant to act where it's needed.
I would say to give it a try like I did, you can always have it taken out if it doesn't suit you.