What would be a better typing experience in landscape mode of a keyboard?

While designing a keyboard app for android, I went through a lot of testing of various existing keyboards. One thing found in common was that typing in landscape mode of every keyboard wasn't very comfortable:

• The keys being more spread out than the portrait keyboard, reaching out to keys with 2 thumbs is difficult
• The keys in left & right extremes of the screen are difficult to access/tap

Seemingly, typing in landscape mode would be a quite a small use case, but it hasn't been optimised.

Some keyboards have contracted the keyboard horizontally in order to make the keys more reachable in landscape mode:

• iOS keyboard for iPhone 6 & 6plus (Apple also gives extra keys on both sides)
• Samsung's default keyboard in some large screen devices

In all, there seems to be very little or no information about landscape keyboards.

Are there any dependable statistics or research on usage of keyboard in portrait vs. landscape mode or the latter in general?