I have an application called Melody Assistant (don't know what it costs now but I spent a €20 on it ten or fifteen years ago). That has a decent default MIDI voice bank. I write the parts straight onto the score and there are plenty of tools to adjust tempo, play accents. The parts I write are melody, piano, 2nd accordion, bass and drums and, depending on the level of orchestration I want, other instruments as required. I don't know if there are limits on the number of parts you can have; if there are I haven't hit it yet.
So you need to be able to read music to do it that way but, if you have the right equipment you can record the parts directly onto the software and mix the balances. I haven't done that with a full on accordion piece (I don't own a drum kit being one reason) but I've done it with some guitar stuff and honestly, it is no better than okay. Producing backing via the MIDI files gives a much better sound and is a lot more intuitive when it comes to mixing.
Once I've got the track finalized you can poke it out as an MP3 or WAV.
What I then do is create a video file (MP4) with slides showing me what part of the song I should currently be playing (e.g. The Dashing White Sergeant - Part 1) and what the next few parts are. Getting the display timing write can be tricky but once it is done, I can use it on standard karaoke software. I have a DJ/Karaoke package call Dex3 (that was a bit more expensive, about £120 if I remember) which has the facility for playlists and automatic queuing of tracks. My idea is that when I put together an entire show, I can use that software to control it at gigs.
Back to the track creation: I think the big advantage of doing the parts individually is that I can develop my own sound in terms of second accordion registers; I will use bass runs that should be unique; I also like to write in harmonies which you wouldn't necessarily get with a store bought backing; I put in the piano parts as I would play them which is close to standard but has my own nuances. And when you cobble it all together; the over sound should be traditional but nothing like anyone else. Once I get myself sorted with a SoundCloud thing I'll pop a couple up to see what people think and I'll be happy to answer any questions (as best as I can).
The disadvantage with backing tracks is that, once you start them you are locked into that program. If you are playing with a band you can always have that look round and shout out a different song or wind it up quickly if something goes wrong.
Never put off until tomorrow that which you can put off until the day after