Dave
If you use a midi as the accompaniment, then you should know that you are stuck with staying exactly to the recorded arrangement. That may or may not be an issue for you.
I did not listen to all of the songs you posted, only the first one, and my initial thought was that this was not so way out there that a suitable style could not be found. Of course it would not be exact but with some editing of voices and style tracks, maybe some cut and paste between styles, possibly get close enough with minimum effort. Especially bearing in mind you can add riffs and phrases by playing along with it.
If you really want to make a midi that is very close to the original accompaniment, another way is to start with a very basic style - cut out unneeded tracks to get it to a minimum - maybe just the rhythm and bass, then record that as a basis with the correct chord changes, then add some additional tracks using multi track recording to customize it. I find this a very fast and simple way to make a midi.
Here is an example. It sounds like a highly customized track by track midi, but it's not. Its a hybrid starting with a basic style driven accompaniment then adding just a few tracks. This can be done so quickly compared to starting from nothing.
https://app.box.com/s/kp3mhz4b6hyy1lgrtyim5mber7xwvio5 Mike