## Retina, <s>54</s> 53 bytes

    T`au`ie`y.
    wa
    we
    T`\oeuia`ao
    T`ko`stn\hmyr\w`.a
    ^a
    ka

[Try it online.][1]

### Explanation

Wooo, showing off even more features from today's 0.7.2 release. :)

    T`au`ie`y.

This is a transliteration which replaces `a` with `i` and `u` with `e`, but only in matches of `y.`. The purpose of that is to treat `ya` and `yu` like `yi` and `ye`, respectively, in order to skip the gaps.

    wa
    we

Respect `wa` with `we` to skip that gap as well.

    T`\oeuia`ao

Here is the new feature. When rotating sets of characters, the "from" and "to" set in a transliteration are usually almost identical. So now we've got `o` (without a backslash) to refer to the other set, which allows us to get rid of some duplication. The `\o` just stands for a literal `o` in that case. So the two sets expand to:

    oeuia
    aoeuia

The extraneous `a` in the second set is ignored and the vowels are replaced cyclically as expected.

    T`ko`stn\hmyr\w`.a

This does the same thing for the consonants, but using `o` in the first set (just because we can...). `h` and `w` need escaping because they are character classes. The expanded sets are:

    kstnhmyrw
    stnhmyrw

The `.a` restricts this operation to syllables that end in `a`, i.e. those that wrap to the next line of the table.

    ^a
    ka

Finally, we replace a single `a` with `ka`, because that case cannot be handled by the previous transliteration.

  [1]: http://retina.tryitonline.net/#code=VGBhdWBpZWB5Lgp3YQp3ZQpUYFxvZXVpYWBhbwpUYGtvYHN0blxobXlyXHdgLmEKbWBeYQprYQ&input=YQppCm8Ka2UKc28KbmkKeWEKeXUKeW8Kd2EKd28