I installed my own and built my own surround, not because I'm skilled, but because I'm ... uh.... well, that's kind of what I do. (I also built/G.C./finished my own house.)
Anyhow, my first thought is that you're going to spend some money on this anyways, so I wouldn't half-uh-"rear-end" it. I assume that you have a masonry chimney that you want to retain, putting a vent pipe up that stack. That makes sense.
However that hearth seems really high, way out of proportion to the rest of the fireplace. And with the windows on either side of the fireplace, you're really constrained horizontally, i.e. you can't expand the fireplace and make it wider, to make it more proportionate to the size of your hearth.
The only thing that you're really saving with your plan is the top of the hearth and the mantle. The mantle is at most a couple of $100 to replace, so I wouldn't plan the project around that. The top of the hearth might be saved, if it's removed. The mantle itself could be saved, so you could just replace the side trim pieces to increase the height of the mantle (i.e. it's standard building store stuff, easy project to do with a decent saw).
So, if it were my house, I'd consider rebuilding the hearth maybe half as high, try to save the hearth top (if you really like it that much), knock out the floor of the never-again-to-be-used fireplace, and open the fireplace up vertically, so that you can install a proper sized fireplace insert. Or perhaps, build it level with the floor, with either no hearth (patch the existing wood floor) if you like that style, or a stone-tile hearth of embedded at floor level, again, if you are interested in that kind of style.
I'll attach a picture of my own project. It's not the same style as yours, but your dimensions (" At 41 ¾” wide by 33” high") were very close to my unit's face.
My "direct vent" insert had a black steel facing above and to the sides, 10" from the top to just under my mantle, and 2.5" out to the sides. I just installed CBU (concrete board, flame resistant) over it, secured by high temp glue and mortar (versus screws, because that steel facing can't be pierced; safety issue), and then installed the stone over that. That enabled me to create a decent sized fireplace surround, 16" on the sides, and 10" up to the bottom of the mantle (minimum safe distance). A direct vent insert wouldn't work for you, of course, due to the retro fit (i.e. mine was a self-contained, sealed, zero clearance "appliance box"). My picture illustration is just to allay your concerns about a steel facing; most gas inserts don't have those anyhow, i.e. they fit inside the fireplace box.
Just as a warning, you may be constrained by the depth of your current fireplace opening, as well as your width and height. I recommend finding units you like on the internet on Amazon, Ebay, or a fireplace specialty store, that seem like an appropriate size, and then look at the installation manual to figure out exactly what the size/installation constraints for the unit are. You may have to go smaller that you intend. You can certainly have pro's do all this work, but it's a good idea to know the installation and safety constraints yourself, because in this situation, you're essentially the general contractor. Not every pro hired is infallible, and there are critical safety/health issues involved.
FYI, I compromised my design for various reasons. I bought a house that was an abandoned build, re-permitted everything and rebuilt it to code. The fireplace kickout was already installed (i.e. not rebuilding that structure), and during the rush to get the house done by winter, we just built a platform, threw the DV fireplace unit on it, and hooked up the gas and electronics. When I finally finished the surround this spring, some 3 YEARS (!!) later, a lot had changed. To make a short story long, I'd have preferred to cut that hearth down even lower, maybe even level with the floor with inlaid slate. However, that would have required reinstalling the approximately 170 lb unit, AND maybe the gas line, too. I'm working solo, and didn't feel like setting up the rigging to move it. I also would have preferred a 2" slate hearth, but they ran between $1000 and $1500, plus ridiculous lead times during building season, AND weigh a ton, I went with the 16" square natural slate tiles. Since our theme was "Northern Idaho Rustic", it worked for us. (Still working on reinstalling the gas logs, firebrick backing, and etc.) Note that the colors are skewed due to poor lighting, it's a more consistent, darker color (as is the engineered wood flooring).
In summary, I'd think "outside the box" for your design, and forget about cost. Come up with a couple of different designs and solutions you like, research your target insert, and THEN back the project plan into your price parameters, reusing or substituting what you can. You may find a plan you prefer better than your original compromise solution, for not much more money, particularly if you're hiring a pro to do the work. Better designs and plans = money saved in the long run. Find the unit, identify the unit's requirements, identify your design preferences (i.e. mantel, hearth, exterior stone), bid an HVAC/gas installer to install your insert (he'll pull your permit), and then bid the stone surround work (i.e. find a guy with references, he'll usually direct you to vendors, and get your materials). Get everything bid out and sourced, before you start anything. Every quote will teach you something (or provide you better questions to ask).
FYI, I installed my unit, i.e. a "floor model" 30,000 BTU DV fireplace insert with fans, temp controlled automatic electronics, plus materials (lumber, CBU, fasteners, slate, etc), the original HVAC/vent/gas and carpentry labor, for about $2000, plus/minus a few $100. The cost of this unit alone is about $3500 to $5000, plus the rest of the material and labor costs. I'm certain it'd have cost at least $8K to $10K to have this installed by a pro or fireplace specialty store, including all parts, material, and labor.
Anyhow, just my 2 cents. Good luck with your project.
The double walled pipe isn't cheap, but it is an almost "certain" anti-vapor leak solution (i.e. just install it correctly).