Way to go! The first time is always the hardest. Next time should be much easier, though I would go with some industrial rubber safe lubricant rather than detergent. If any of you guys ever need some tires and you just cannot track them down, definitely check out
https://www.kenjones.com. They have come through for me many times and they were there for me for my first tire change about 2o osome odd years ago. All the best!