This is definitely firm, but it was game-changing for both my husband and I: buckwheat hull pillows. I made ours, but there are a number of companies that sell them.

As a fellow side sleeper, it's the ONLY pillow I've ever tried that gives me neck support. You kinda shape it to your head/neck when you lay down and then it just stays put, it doesn't shift or go flat. It doesn't end up feeling firm. I feel like my muscles all relax because they're actually supported. I stopped waking up with tension headaches. It's crazy!

I haven't made any changes to mine (since I made them ~5 years ago), but occasionally my husband wants more hulls in his. I just unzip and add more. I bought the hulls for cheap at Natural Grocers.