Seems odd that yna gets contracted even though it's not immediately proceeded by a vowel...is this just a relic of common usage?
It's a common effect in the spoken language. In fact the beginning of this sentence is also contracted.
The full sentence is :- 'Doeddet ti ddim yna'
The contraction reduces 6 syllables to 4, which is useful in conversation.
As a native this sounds odd to me. I'd be more inclined to contract it to "D'ot ti'm yna" (spoken, not written)