I have no doubt that the EK50 will do very well for the market it is aimed at. The equivalent Yamaha has menus galore and there is a lot of faffing around making changes and from the videos that I have seen so far the Korg does seem to be far more simpler in its operation. Probably due to the process involved in using it, it is probably more like a Roland Go series on steroids.
That said given what you want in a keyboard I do not think that it is the keyboard for your needs.
Prior you have quoted Arrangers which do operate around Style mode but for the serious Musician fortunately with the Korg PA there is the next level with the
PA series and that is using the Songbook feature which in turn leads to your own Setlists.
Using a source Style, modify it and save it as a new Songbook entry, then change Keybord Sets, Pads, Intros, vars, fill, FX and Eq then import an audio backing track then save the Song again and then all these settings are saved with the song. Add the song to a Setlist and in a live gig simply call up the Setlist and select the next song in said list and everything is there for you to start playing. If you want to change Instrument voice/sound there are the four option avaialabe via a single press of the appropriate button, if you want a different instrument then that involves a little more menu digging but without this affecting the style or backing track that is being played.
Is a PA though for your needs, again I am not sure, a Synth/Workstation will certainly do the tasks, but one of the main issues with lower cost (and hence features) is getting a seamless transition out of the keyboard when changing Instrument Sound/Type during a Song or during playback of a backing track. You will need to check out these further.
Certainly you are unlikely to get what you seem to require with a low cost keyboard.
Can I suggest that you research further but at the PA700 and Roland FA series level of cost.
Can I also suggest that you start off with looking at the King of Keyboards the Korg Kronos, watching the tutorial videos on using this amazing keyboard will set the standard and you can then compare all others against it. There is a new Korg Kronos LS model which is smaller and easier transportable and with a lighter key action.
Good luck