Edit: Since this needs to work on a tactile platform, maybe you could add a separate "toggle descriptions" option that would allow the user to see the button labels, and then toggle it back off to remove the clutter for everyday use. This isn't as user friendly as the tooltip, but should still be workable.
Original Answer: Assuming this is a desktop application, a common way to handle this problem would be with a tooltip. You can reduce the button label to only one word, or even a representative icon, and then add the more detailed information in the tooltip.
The downside is that the user will have to hover while they are getting oriented in the software. However, in the long run it reduces clutter and streamlines the workflows for experienced users.
I might get some disagreement here, but I think that the user will be more than happy to hover if they need clarity, if it means the buttons won't be too large to all be shown face up.