> (though salary isn't posted in the ad)

Might be the problem ...

> the work being a higher percentage non-code is what's causing us trouble

Might be another problem... are you recruiting a PM or a Software Eng ?

> - Take-home technical assignment (~4h) or similar at candidate's choosing

I've personnaly stopped doing those. Either they are very far off the job either too revealing. And generally taking way too much time.