Got a zip code? (To more closely specify the local climate, which varies a lot within NM.)
I assume this is a 2-chamber variant of your stuff?
With an all-masonry wall dew-point calculations hardly matter- masonry isn't susceptible to moisture and as long s you don't have highly vapor-retardent interior finishes like vinyl/foil wallpapers it'll dry toward the interior under any circumstances.
For a foam-over job with rigid foam the thickness you can attain depends a lot on what you intend to do for exterior siding, since the fasteners for the foam will be carrying the weight. The mechanical strength of stucco-clad pen-tile probably quite a bit less than that of concrete, so hanging stucco 5-6" out probably isn't in the cards. But 3"(R12) maybe 4" (R16) of EPS would almost surely work. The fasteners would have to penetrate both the old stucco and the tile, but if all they're holding is metal lath fairly snug to the EPS you could get there with the masonry screws 16" on center. It all depends on the strength and integrity of the type of pen-tile used. If yours have an almost glassy hard-fired surface it's much stronger than the dull earthenware/terra-cotta look. If it's a softer type you may need to drill all the way through and use a through-bold with a flange/plate on the interior side to distribute the load over the interior face of the tile block.
Assuming your R5 estimate is about right, 3" of EPS would yield a whole-wall R of about R17, which would beat 2x6 timber framed/wood siding construction (~R13-R14 after the thermal bridging of the framing is factored in.)
An EIFS approach would be much lower weight and you could go fatter, but an EIFS finish wouldn't match the original stucco very well. But as a low-mechanical load system it might be the cheapest way to go with the least number of mechanical strength issues.
With the increased wall thickness you'd have re-work the window & door flashing on that side, but with an all masonry & foam approach the wall would be fairly tolerant of flashing faults, even if the window frames had issues.
If the additional wall thickness needs to be more structural & self-supporting or you want to go higher-R there are SCIP (structural concrete insulated panel) systems out there to build up wire reinforced concrete skins as the scratch coat for the stucco, but that would require building out the footing of the foundation to support it, eg: http://scconcretehomes.com/ Clearly SCIP is more expensive than a 2-4" foam-over with EPS and metal lath stucco tied to the original wall with masonry screws, but it's a very solid & durable way to build an insulated stucco clad wall.