177.5 is gonna be kind of long for a road conversion going fixed, which is a shame. Save that set for another road bike later on.

The Luna has vertical drops, IIRC. Your best bet would be to run it SS with a tensioner. Another option is to run it fixed with an ENO hub.

Another idea. See if you can trade the crankset for an ENO wheel. Then get a shorter crankset on the cheapy cheap and you'll be set, assuming you have everything else you need.