Well you could write lyrics for one of their melodies, and then draft a new melody for the lyrics. This will give a new song that in essence has the same vocal rhythm or similar.
Your issue would also suggest that:
You should research your target writers more so you can accurately characterise their writing style. For example:
Are they fond of specific song forms?
Do they use standard song forms or tweak them? Are there common element to the tweaks?
What characterises their use of language?
Do they use metaphors? Similes? Etc. simple or complex rhyme schemes? Internal rhymes? Alliteration? What about topic choice? Perspective? Tense? Literal/abstract? Message? How about the use of hooks? Do they use a specific writing technique like "cut up" or "fold in"? Do they use a process? If so, how tight or loose is it? For example do they have draft and edit cycle? Other phases?
Once you have the answers boil it down to a writer intel sheet you can easily refer to during writing.
Sometimes finding more about what motivates their writing will help. Where do they find their inspiration? Newspapers? Books? What about writing environment? For example in a coffee house, or outside in peace and quiet. Bear in mind they might draft and edit in different writing environments.
Just some thoughts off the top of my head.