Bill- welcome to HRS
I guess my first question is what is it about the Korg that you're dis-satisfied with? and what do you think you will get at "the next level"?
outboard pre-amps- generally most of the internal preamps on mixers are not the highest quality- if they truly were "world class" the cost would be much greater, so better pre-amps would improve the signal chanin, but....I've seen the Korgs but never used one- can the internal pre's be bypassed? or does it have inon-preamp inputs? If not, a better external pre-amp won't garner much improvement as the signal will still have to go thru the lower quality internals. If the input channel has a input gain/level pot/slider (not the channel/post volume fader)and it still controls your input levels then atleast some portion of the internal pre-amp circuitry is still involved
Room acoustics- yes, if thought and some research is put into this it will make a difference in the room you record in, as well as the room you monitor mix in . You can "kill" a room by getting a bit carried away and just buying a carton of Auralex acoustic foam and sticking it up here and there may help a little but it's definitely not the right approach
as you've said you don't have time for reading or experimenting my gut feeling is you're better off staying with what your doing and accept it as-it-is. Everything in recording comes with a learning curve, while some of the methods seem intuitive for some, most are learned skills, otherwise the George Martins, Quincy Jones, and "insert famous engineer producer here" would be nobody special!
ProTools would work for you (I am a PTLE user on a Mac), if you don't want to deal with the proprietary limitations that ProTools has, then Logic or Cubase , or Reaper would work well, but each has differences, strong points, and limitations, and there's knowing the outboard gear so you can get the best results-
would you just put any mic anywhere in a room, hit the record button and tell the musician "go"?