Ran another test with both quantity discount and group discount involved. In this test, I ordered a non-quantity discountable product and a quantity-discountable product on the store-side. Both products subject to group discount. Subtotal, quantity discount, group discount, shipping, tax and order total were correct. After EO entry, the totals were all the same. Now, instead of adding any products, I just clicked update. The subtotal, quantity discount, group discount, shipping and tax were correct. The total was too low by an amount that equals the tax on the sum of the quantity discount and member discount!

So something goes wrong when update is clicked and a quantity discount is present. It doesn't matter if the quantity discount product was added by EO or was in the original order, the result is that the order total is too low by the sum of quantity and group discounts. If group discount is not present, the total is too low by the tax on the quantity discount. I have no way of seeing if any other discount types affect the total.

As a side note, on the EO page, the quantity discount is editable and in a box. There is no minus sign displayed and the number is displayed to four places to the right of the decimal point. The group discount is not editable, there is a minus sign and no box. The value is displayed with two decimal places. Not sure if this is significant to the problem at hand.