The temperature of the duct matters- upper service temp of XPS is ~160-170F, but shrinkage can occur over time even at lower temps. If you can slip in some half-inch foil-faced polyisocyanurate it's rated for use up to over 200F (and won't deform until ~300F).
It might be easier to make it air-tight by insulating the gap with FrothPak (1.5lb density polyurethane), which is good to about 240F. At a half-inch of thickness a
12 board foot kit from a box store would cover ~24 square feet, and you can use any extra to seal your rigid foam to the foundation & foundation sill, etc. Any spray polyurethane will pretty much glue your duct to the wall though (it's a similar chemistry to Gorilla Glue.)
If you can use 1.5" EPS rather than 1" XPS it's usually a bit cheaper, and is more environmentally benign, since EPS is blown with pentane which has about 7x the greenhouse potential of CO2 rather than HFC134a (used in nearly all US XPS) which is something like 1400x CO2. At 1.5" it's ~R6 (any density), and has at least as good an up-rating curve as XPS with rising temp. When it's below 25F outside 1.5" of EPS on the above grade portion (which is most of your wall in question) will be performing at ~R7 in your stackup. With R15 Roxul and 16" o.c. studs, with the thermal bridging of the studs factored in you're looking at about an R15-R16 "whole wall" value.
Alternatively, if you can find a source for reclaimed roofing iso (polyisocyanurate with fiber or paper facers), that stuff is about R5.5-6 per inch and denser than the foil faced goods you find in box stores. At 3.5" you're at R20, and you can hold it in place with 1x furring through-screwed to the foundation with 5" Tapcons 24" o.c. on which to hang the gypsum, and you'll get pretty much the full R20. Reclaimed iso is typically 25-35% the cost of virgin stock, and would come in at about the same cost as virgin stock 1" XPS. I have several vendors in my area advertising reclaimed roofing foam of various thicknesses on craigslist, but I also have a local outlet for insulationdepot.com (which will sell small lots if you have your own truck, but will ship nationwide in larger quantities.) It can even be cheaper per R per square foot than R15 Roxul.
It comes in a number of standard thicknesses, but you'll need to dig up a source for longer TapCons than what's usually available at box store at foam thicknesses over ~2.5"/R15. (Online vendors, other local hardware stores, etc.) The exposed edge of iso needs to be 1/4" or so off the slab if you're not sure about the moisture content of the concrete & subsoil, since it can potentially wick up moisture over time, whereas EPS/XPS won't. (A single layer of 3" roofing iso was the retrofit solution at my house- it took more than 15% off my heating fuel use!)
With your studwall approach, cut some 3.5" strips of the foam to put under the bottom plate of the studwall as a capillary & thermal break, and through-screw the plate to the slab with TapCons. That will keep the framing drier & warmer no matter what your sub-slab conditions, and you won't have to use pressure treated timber.