OK. Initial conditions are that you don't have nylon string guitar, you can only record two tracks at a time in a rectangular untreated room.
No amount of treatment in post is going to let you match sample posted. From a work flow process I'd initially just record anything . . . best guess . . . and let client listen to it over period of more then a single listen, single day and use their response to figure out 1. is it worth pursuing (it is possible their expectations can not be met) 2. if it can be done it tends to help to move in direction of what is acceptable to client.
(I'm not suggesting you use a clients rigorous critique as micro managed aesthetic arbiter . . . but it surprises me (even now) at what a client actually hears (and does not hear) and it is possible that without spending thousands of dollars & hours you can provide perfectly satisfactory results)
That said there are a couple of things to try. If you only have two simultaneous tracks (dual mono or single stereo) in a 'poor' recording space don't sweat the stereo recording it is probably a battle you can't win . . . if you absolutely have to have stereo, then learn the piece well enough so you can mix and match multiple sessions
what mics are you using for stereo?
first thing I'd probably try would be to orient playing along a room diagonal, even so room is small enough to make anything but close mic'ng problematic. If your room lacks wood floors you might try buying a sheet of half or three quarter inch plywood use that as the performance location. If the MSH-1m is one of the naiant omnis I'd use that close . . . positioned above angled down focus somewhere around where neck meets body . . . spend a bunch of time on day of session looking for a spot where that single mic sounds the best. If you have more then one additional mic I'd spend some time finding which one seemed to work best pulled out into the room as natural ambiance. If you have access to a figure of 8 condenser or ribbon, paired with close mic you can try some M/S-esque stuff on mix down.
In post the options become, if not infinite then limit is certainly intractable to determine. If you are not happy with reverb options look into some convolution. Build a pseudo stereo with some EQ & delay on a doubled track, then gate your ambiance track, EQ it differently and then dynamically, (and it can be subtle or not, both can work) mix it in to taste
Rhythm track might be pretty verby, with your so called lead track fairly dry, with just a touch of a verbed doubled track brought up on some transitional sustained tones, etc. . . nor is 'artificial' necessarily bad, the sample you included does not sound particularly 'natural' to me . . . it is just a matter of what works.