Writing as someone who's been through this exact situation --
1. You don't need a lawyer to write the letters I described in my post.
2. Demanding "pain & suffering" will be seen as frivolous and won't advance your cause. Stick to what you actually unconditionally earned, i.e., the cash back.
3. Citi's opening offer to settle will likely be a flat $500; probably good to think now whether that will be acceptable to you.
4. For various reasons that I'm not going to detail here, filing for arbitration with AAA is better than JAMS, imho.
5. T&C applicable to my card says that Citibank will pay my share of the arbitration fee for Claims of $75,000 or less if they are unrelated to debt collection
6. If you don't understand that the idea here is to get reasonable settlement in lieu of actual arbitration, this approach isn't for you.