Seeing this particular phrase 力なくなく for the first time myself, I cannot think of it as anything else but a kind of 畳語 (reduplicated words/phrases) version of the adverbial phrase 力無く (without strength; limply, exhaustedly), with the meaning unchanged.
Using 力なくなく as double negative (i.e. not without strength) would be pushing it both grammatically and stylistically, and 力泣く泣く leaves 力 abandoned, disjoined from any part of the sentence, as you suspected.
Now, as 畳語-fying goes, 力なくなく seems atypical, but I don't know of any rule that says it cannot be done, and Google search shows that it has been done by published authors too (力なくなく and 力無く無く), unless these examples are just typographical errors or another construction altogether -- but it doesn't look that way.
I believe it's done more for rhythmic effect than emphasis, if anything. The seven-syllable variant makes the flow of the sentence a little more... lilting, at least to my ear, though the scene it describes (a disheartened and exhausted warrior making his way back to his castle empty-handed) is just the opposite of that.