How to reduce propyne selectively for the trans product
As you point out, a dissolving metal reduction using $ \ce{Na}$ and $ \ce{NH3}$ in the presence of a proton source such as $ \ce{tBuOH}$ is able to reduce a disubstituted alkyne to the corresponding trans alkene. 

The mechanism is understood to go via the following stepwise mechanism:



Both protons on the product  come from the $ \ce{tBuOH}$, rather than the $ \ce{NH3}$ as suggested in the comments, so in theory, using $ \ce{tBuOD}$ would give you the desired product. 

One issue with this however, is the ease of exchange between $ \ce{H}$ and $ \ce{D}$– any residual water present would be able to convert $ \ce{tBuOD}$ to $ \ce{tBuOH}$, which would then give you the protonated rather than deuterated product.  Experimentally, you'd probably end up getting a mixture of products with varying degrees of deuteration (mono and di).