Hello Ashley!
It sounds like you were on the right track by transplanting into better draining soil. That can quickly cause root rot which would greatly impact your plant. By the looks of your palm and the information you gave us, I would say that a good slow release all purpose fertilizer such as Doctor Earth All Purpose would help to perk up it up. Be sure to only do this during its growing season. Another suggestion would be to prune back the stalks that have dried so the palm can focus on growing new, healthy growth rather than putting its energy to support the old, damaged parts. Always take care in removing any old, dried leaves like the ones you described for that same reason as well. If the brown spots continue to pop up and worsen to the point where it resembles leaf spot, cut away all affected areas with sterilized equipment and treat before it has time to germinate with products such as Safer Garden Fungicide located on our online website. Good luck with it and I hope it starts shaping up soon!
Check out our Dr. Earth All Purpose Fertilizer and Safer® Garden Fungicide here:
https://www.planetnatural.com/product/life-all-purpose-fertilizer/
https://www.planetnatural.com/product/safer-garden-fungicide/
Also, take a look at our page on Leaf Spot if you would like more information and what signs to look for. https://www.planetnatural.com/pest-problem-solver/plant-disease/bacterial-leaf-spot/
Good luck!