Personally, I wouldn't buy another incubator for a few quail eggs. You are right that lockdown is in 2 days. Shipped eggs should be rested for a day (pointy end down) to get their air sacs to the top again. Ideally, you leave them upright for a few more days in the incubator before starting to turn them. By then, the first batch are hatched and you can setup the turner for the second batch.
Is this a Hovabator with turner? If so, pop out one of the rails and put the new eggs on it (no turning). When you remove the turner for lockdown, place the new eggs (still on the rail), in with them. After they hatch, move the turner back in and your all set.