IF the income reported on the 1099MISC is tax exempt, you can reduce your taxable income using the information from VolvoGirl at <a rel="nofollow" target="_blank" href="
https://ttlc.intuit.com/questions/3799205-i-received-a-w2-with-wages-in-box-1-for-income-is-not-subj...>. I am not familiar with EIC and cannot comment on that part of your question. Reducing reportable income to reflect only the amount that is taxable shouldn't affect benefits under other parts of the tax code.
