"not a single rivulet of light does my heart seem to want to let it be furnished with."
This is an extremely odd sentence, although I would not say it's grammatically wrong. First, let's study the predicate "let it be furnished with."
To put that in a literal, rather than metaphorical, story, consider:
"I own the room, so John has to ask me permission to put furniture in it. There is a chair that I like a lot. I want John to put in the room. So you can say of the room that this is the chair that I want to let it be furnished with."
I hope this makes sense grammatically, even if it is a weird story. Now we have the same, but metaphorically, with the heart being the landlord, the light being the chair, and the monster being the room.
In addition to the odd "let it be furnished with" construction though we also have
"(not) [object] does [subject] [verb]."
I don't know the name for this structure (it reminds me a bit of Yoda in star wars), but it's not rare in music and poetry (often in poorly-written poetry to get a rhyme and give an old-time effect) while never used in speech. It is more common with other auxiliary verbs (e.g. has or will instead of does.)