If the 1099-MISC shows the income paid to the business name and you have an EIN for that business, then there's no question that you are "in fact" self-employed. Reporting any other way will raise eyebrows at the IRS. One doesn't get an EIN for a hobby. You need to report this as the business income it is. The fact the business may show a loss in 2018 because of expenses doesn't matter. By reporting your business income/expenses on SCH C and since the business has no taxable income, you will not have any increase in your total tax liability. But you do need to report it for the business income it really is now.
Also, unless you're a one man band, you need to look at forming a partnership for this band. Otherwise, since the EIN of the current business is tied to your SSN and "only" your SSN, that makes you alone personally liable for the taxes. Forming a partnership is fairly simple. But if your state taxes personal income you should seek the help of a professional in setting up the partnership on paper. Then for 2019 taxes you'd file a 1065 partnership return and each member of the partnership will receive a K-1 from the partnership so that each member can report their share of income/losses on their own personal tax returns. Then you don't have to bear the entire brunt of everything on the tax front.