I don't know the Lavezzi
but here is my 2 cents worth of input.
I am guessing you can't mouse the ends and pull them through, so you are looking at the two broken ends. If I am sending wires along through small spaces I have two tricks.
The first is to get some galvanised wire from a hardware
store. Check out the bendiness with consideration of your hose. Hopefully it is straightish. (Actually if it is straight then all is good - use fold up tent poles to push through a small piece of venetian blind cord and you have you mouse). I can't really see how the hose could have a bend in a steering
cable so the wire, or tent poles could be good to get the VB cord through, then you pull the new spectra through.
The second is interesting. Put a vacuum cleaner on one end and push a piece of string - maybe tie a very small piece of rag on the end - down the other end. Electricians use this method to place a mouse down conduit. This is the most fun method.