The section of your paper that begins to present an analysis, starts by claiming the result. This is not good. It is like you start with a result and then seek to prove it. The scientific method is to do the analysis, and then find the result.
This text is what I am referring to.
"A Large Increase in the Distribution of Household Income
If there is suddenly a large increase in the distribution of household income, basically meaning that suddenly there is less income inequality in an economy, then there could some harmful effects."
To really understand the distribution of income, you have to follow the labor share number. Let's say that a lot of money is distributed to lower incomes with a higher propensity to consume. Demand will rise as you say in your paper. But then that money becomes re-distributed according to labor share. If the labor share of income does not increase, the money will simply return to capital owners, and wealth inequality does not change in the end.
The key to reducing wealth inequality is to increase labor share of income. That process is a slower one than simply a one time shot at giving money to lower incomes. Increasing labor share is a more gradual process of balancing wages and salaries throughout the economy. It may involve government action and it would certainly involve labor power to obtain higher wages. Both of those are weak at the moment.
Even if minimum wages are increased, it takes time for higher wages to adjust. There will be resistance to adjust higher wages, since there is no legal mandate to do so.
So increasing labor share is not a sudden occurrence. The premise of your paper is not properly focused on labor share.