The problem is that you have to go from low-speed regime in the atmosphere (the balloon), to a high-speed regime out of the atmosphere (~7000m/s). The low forces available from a solar sail don't allow this to happen quickly enough.
At an intermediate speed it is either destroyed by forces from interacting with the atmosphere or it is insufficiently supported and falls back down.
My hope was not to have to get the high speed regime. Instead use the solar thrust to nullify and constant help the probe to get out the earth.
The problem is that solar thrust is very low, so you need a huge surface area to capture it. Let's say you had a 1kg payload in the upper atmosphere at low speed. Without a balloon, you need the sail to counteract the weight.
Unfortunately, the force available from light is low. Discounting all sail losses, it's about 8.25µN/m^2. If we imagine a magical solar sail that is massless, then to counter the payload weight it would have to be:
$$A = \frac{W}{P}$$
$$A = \frac{9.7\text{N}}{8.25\frac{\text{µN}}{\text{m}^2}}$$
$$A = 1.1\text{km}^2$$
So a perfect, massless sail would still need to be over a square kilometer in size to counteract the weight of a kilogram. This is simply not practical for such a small payload. Add in the mass of sail and it becomes impossible. Adding in ionic pressure doesn't help significantly.
Only after you reach orbit (when weight no longer is a problem and tiny forces can do useful work) can such a low-thrust device be useful.