I feel your pain. But a custom design job is hard to unload on someone else, as it is not a "custom" design to the new client. People forget that "custom" doesnt mean "unique" it means "tailored", as such it is really difficult to push unsold design you did for someone else as "custom".
[ I do have a question... how did you incur costs designing a logo?]
I will share 2 pieces of advice:
1) Charge Custom jobs by steps. Let the client keep whatever you do even if he bails, but at least you didn't end up working for nothing ( I hate when it happens).
2) In lieu of that, keep discarded/abandoned design as portfolio pieces and and an inspiration junkyards. Explicit in my contracts is that the client gets only the design they pay for.. so what happens to all the brilliant concept the never make it past the draft stage or from clients that defaulted? They go in my organizer by concept..if BY LUCK i find a competitor of the client hat just loves the rejected /abandoned piece great... if not I can dissect it for quick inspiration for a paying client with different needs. Taking a cue from nature, I waste nothing.