I've never needed to really take effort to improve mono compatibility of my projects, been lucky, but now I need a little advice.
I have four guitar tracks (+ AD drums and Manybass bass) as follows:
- A pair of strummed (electro)acoustic guitar  mono tracks which are from a single take, one recorded via mic and the other through an FX pedal. Then timing of these has been edited, so they're not in their original positions. These two are routed to a bus hard panned.
- A supporting mono track created with Orange Tree Steel Strings VST. Routed to master bus.
- A solo track/Orange Tree, routed to master bus.
 
When switched to mono, these guitar parts suffer disturbingly.
Now I'm confused about the proper easiest method to cure the issue. How to spot the (worst) troublemaker,
where to stick the goniometer (in Master bus with drums and bass muted?) etc.? Does the goniometer of, say, Flux Stereo Tool do, even though that's (AFAIK) meant for stereoizing mono tracks?
Or should I just go by ear nudging tracks back and forth by about 10 ms?
 
Thanks in advance!

Your mono Orange Tree tracks shouldn't be causing a problem.
 
But there's a definite possibility that the other 2 tracks are causing phasing issues "one recorded via mic and the other through an FX pedal"
 
Best bet by far is to record a second, duplicate track and pan it to the other side of just one of the originals.

I use a small Auratone type speaker to check mixes but it is also great for mono testing as it sums L+R.  I find one speaker shows up mono problems better than two speakers in mono.
 
I would start with the tracks that have two tracks for the one source and try a few things.  One is reverse the phase (polarity) of one of the tracks when summed. Sometimes this makes a big improvement.
 
The other is try dropping out one of the tracks and see if the basic sound stays intact but there won't be any phase issues because there is nothing to cause the sound to change. eg the guitar that has been recorded via the mic and the pedal.  Try using one of the tracks only.  You might find it sounds better anyway.  Just because two tracks have been tracked it does not mean you have to use them.
 
Another option with the two tracks on one source is feed one of the tracks into a filter to separate out bottom end and higher end and try reversing polarity on one of the filter outputs as well so you are only effecting the polarity of part of the spectrum of one of them.
 
I would avoid slipping tracks in time though, I think you are messing with things a bit here unless you can get a consistent good solid sound without any obvious flamming going on.
 
Tracks that have been overdubbed although playing the same parts ie doubling should give you much less trouble.
 
Mono compatibility is important and for me when I hear nothing changing in mono and things are still sounding robust then this goes a long way towards a better mix in the end as well.
 
I deal with this with some synth presets as well. eg effects etc... Sometimes they do dumb things like reversing polarity of one side to create a wider image but it does not play so well in mono. Altering the polarity of one side often fixes the issue quite well resulting a solid robust sound and still wide at the same time.

Thank you for the answers!
I was lucky again. The problem got nearly solved by a nudge of 10 ms, found the right one by trying different combinations. I'll do some further tuning with phase reversions, at least to educate myself.

As a broad rule of thumb, two similar tracks will have minimal phase-cancellation issues if they are 20ms or more apart. The problem is that you'll lose the Haas effect, but it's the Haas effect that plays havoc with mono-compatibility in the first place.