Disclaimer: The following is a heretical statement and there are several people who will undoubtedly strongly disagree with me on this point. This is my personal opinion and I am not making a recommendation. You’re the decider.
You could do some root work and the tree will probably be ok, providing that you are attentive to its needs and neither underwater nor overwater it. However, if you do this, you are rolling the dice and there is some risk that you might kill your tree. Are you comfortable gambling your $22 that you spent on the tree? The upside if it works is that you’ll get your tree settled into good free-draining soil this year and the tree will have recovered by next spring and you’ll be all set to move on to step 2 of your master plan, whatever that is, during next years’ growing season. The downside if it doesn’t work is you end up with a dead tree for the compost pile. I wouldn’t recommend repeating this in the future once you’ve invested effort in training the tree, but as a one-time thing to jumpstart progress on a cheap nursery tree, it’s something I have done before. Just answer Clint Eastwood’s question. Do you feel lucky?