It sounds like trouble to me! Also with you going on vac shortly after the first baby starts the chaos will just run on longer. What about advertising the 2nd one for Sept start?

You could make it work if you get creative. I know your daycare is in the basement and all the kids sleep down there. What if you sleep train the babies in different areas (One upstairs and one downstairs?) just until they settle in?

You may be surprised. I could see that they would catch on almost quicker because they would have to e.g. they would both learn quickly that they aren't going to get picked up right away etc. Also, then you don't have the first one expecting the extra 1:1 that happens when they start if you staggered them.