Ok, let me try and revise it.
Hello, I'm [Name] and I am going to reject premise two. (Premise two: There is no morally relevant difference between Jim’s immoral behavior and my indulging in what I reasonably believe is a luxury instead of trying to prevent the horrific deaths of small innocent children.)
The thought-experiment that it is based off of is only a local situation. Premise two fails because it assumes that the conclusion drawn from the local situation can be applied globally. It cannot. When drawing a global conclusion, you must draw it from a global premise.
Because of this, we need to look at what would happen globally if we do, or do not purchase luxuries.
It is morally good to try and improve the conditions of life for as many people as possible. If we want to try and make this world the best it can be, than it is reasonable that the people living in it will need to live physically and psychologically health lives. Throughout history, it is should be quite obvious that humans instinctively want luxuries, and in many cases, monastic societies that attempt self-deprivation often become corrupt or fail. To deny humans these things is a bit counterproductive. So if a degree of luxury is required for us to attain a better world, then it clearly cannot be immoral.
(I have realized that it could easily stop here if he is convinced. If he is not however, then I move on to the thought experiment.)
There is another way to think about it as well. Consider this thought experiment.
We are living in modern society. It is announced that to buy luxuries when you have the power to be charitable is immoral. Everyone agrees with this, and not wanting to be immoral, people donate their money to charities instead of buying luxuries. Slowly, in the developing countries in the world, the quality of life starts to get better. But because the public is no longer buying luxuries, the state in no longer receiving nearly enough revenue due to the lack of sales tax. People downgrade their homes so that they can give more money to charity, and the state is receiving less money from property tax. As a result, the state can no longer afford schools, it can't afford roads, the state's infrastructure is on the verge of collapse. Due to the lack of demand of luxuries, the a large quantity of people find themselves without a job. The state is without infrastructure, the people do not have income, and soon the U.S. drops down to the quality of life in which it once sought to improve.
Whenever we buy taxed luxuries, we make sure that our country survives, something that is generator of wealth. In the long term, both making charitable donations and indulging in luxuries produces more good in the world, than if we were to only make charitable donations.
To end, I give you this argument with premises and a conclusion.
Premise one: It is morally right to improve the condition of as many lives as possible (Obvious Truth).
Premise two: Some degree of luxury and pleasure are necessary to improve the condition of as many lives as possible.
Conclusion: Some degree of luxury and pleasure is morally permissible.