Tom, without seeing the grade, there are 2 solutions that come to mind. The first is to pour the apron you are considering over a concrete pipe drain to either the back, as you are considering, or a French drain. The concrete batch plants in your area should be able to point you toward the appropriate sources in your area. Some of the ones in our area have plenty of concrete pipe and fittings in their yards. Some of the other batch plants are just that, but I'll bet that they know who has the casting operations. One of these sources should point you toward the appropriate source if they can't handle it directly.
The other way to handle the problem is to leave the 2 rows of pavers out and ditch out a run to the down slope the same width. Fill the ditch with coarse rock. Whatever the closest thing to steel mill slag is would be great in about a 2" size. You will have to work a little harder to keep this open, keep tree needles and mown grass off with a leaf blower and the like, for instance. Routing this to a French drain is possible.
These may not fit your needs, but they may point you toward the right solution for your place.