Question for composers/music industry folk/lawyers

I’m a composer working on a project to sell my music nationally and then ultimately internationally. Among my portfolio are a number of instrumental arrangements of popular music songs (Ray Charles/Led Zeppelin/Beatles/current pop music/etc.).

My understanding is that there’s no mechanical license for reorchestration/instrumental arrangements. Is this true? If so, what are my odds of getting the holding companies to give me the rights (with or without a fee)?

I’m also assuming that my arrangements break copyright because I use the melodies…

Oh, and Mods: not sure if this is the right forum. I figured the composers would be more likely to hang out here than GQ…