Veloster N, not the Elantra N, but I agree. I chose Veloster as it's a bit smaller and more likely to have parts that fit without even further effort. I'm not saying it would be easy in the ever so slightest but it would probably be more reliable. It's already built for 275 hp, no internal upgrades needed and if you can get the electronics to work together, no tune needed theoretically if you're using the TCM and BCM from the VN(though you'd need work to get the Fortes electronics like brakes and other electronics to function). It's overall a rather weird idea, but to each their own on what they want to sink their time and money into. If you're going to be silly, at least go full send within the limits of the car. You're not fitting an LS without a sawzall, welder and a shoe horn.
Either way, the LXS loses out on some of the GTs features, particularly the independent rear suspension and overall better suspension. It would likely get out-paced in corners by a slightly modified GT(heck maybe even stock) and if the IVT is still there then acceleration and top speed are out the window too. That being said, the FE had a manual transmission in 2019 and I think 2020/2021 so the IVT could probably be replaced with that. Not sure if it would handle the turbo still, but it would at least be faster for a moment before it blows up.