Overdubbing is something that has been going on for years and not just these days. I simply disagree when I heard it said that the music doesnt sound natural when its done this way..
Does it also mean that ..a musician..particularly a rythem instrumentalist who has impeccable timing , would be considered not good?
The best drummer I have ever heard ..who is a full time studio musician..is often referred to as the "human drum machine" and do you why? because his timing is impeccable, he understands the importance playing a smart drum arrangements, meaing not wailing and flailing rolls at every opportunity, although there might be times when this works, and maintaining consistent velocities on his drum hits which is important in the recording environment.
And by the way the human drum machine comparison doesnt bother him at all but rather keeps a smile on his face.
Dobro, back to your issue. I think overdubbing as was suggested is the way to go for your situation. All you need is something even a recorded click track to help you keep your timing and record everything to that time reference.
Heres something Ive been toying with lately as far as doubling is concerned . I am using it the way I understand the meaning to fatten a sound in its place in the stereo field. As was your original question why pan anyway? Well if you have decided that you want that rythem guitar at 10 ..i would take a "clone" or " copy" of the guitar pan it right beside the one at 10 oclock say 10:10 or 9:50 adjust delay on this dupe until it gets fatter which might equate to loudness. You are gonna hear phasiness at the points where you should here it 2ms- 8ms but even that could be a welcome sound depending on what you are looking for, after all , flanging is simply moving two sounds in and out of phase of each at a set time rate. I think you will find some interesting possiblities with this method. Nothing stops you from adding a third either

And of course theres no restriction as to what effects you can use on one or both copies compression, eq,reverbs etc etc..keep in mind though if you are gonna be performing this stuff live ..you will have to be able to duplicate it somehow

This of course should always be an consideration when recording anything.
Something to consider though...remember...that you have part of your signal from that rythem guitar on the right side of the stereo field..try to avoid placing another instrument or elememt on top of it the right side version...find a new home for it that doesnt overlap your rythem guitar in the left field either ....Try this
and see how you like it..holla back let us know how it goes!