An off the cuff idea that might work? You could take a drain like this that is larger than your original, toss the threaded "nut", cut/grind down the threaded throat to the needed height (essentially the thickness of your new thinset/tile), and insert it when you set your new tile. Remove the original drain's grate. Aside comment: depending on what metal the drain is made out of, prime/coat any cut metal edges to prevent rust.

Also do not recommend a Blue Star. Had a Lacanche for 11 years and loved it. Moved to a new home with a 36" blue star and it is really terrible. The burners flame out, the oven is 36" wide but not that tall making it a pain to put dutch ovens in it and out, takes FOREVER to heat up, roast veg just don't turn out that well (typically undercooked), it's hard to get a low simmer. Yes, the burners are powerful but they have no meaningful range and the power isn't necessary. My Lacanche made great stir fry. Also have to rotate food more in oven to prevent burning. Some of these problems may be oven size and not blue star specific but I've cooked on other 36" ovens in rentals long ago and didn't have as much trouble with the oven. It seems to be made with solid materials but the putting together of those isn't that well done. I'm glad I got a Lacanche all those years ago when we remodeled out first kitchen. Our new home wasn't as lucky. Missing my Lacanche Volnay.

Tileable grates are heavy to lift out for the increased maintenance that linear drains require. Tiles can be chipped on the grate or walls during removal.

I have a solid surface wheelchair accessible shower pan. The drain is in the front, to allow the shower floor and the room floor to meet up nicely. Since my shower stool and vanity stool are the same item, I swing that oversized thing into and out of the shower each time I shower. Between the oversized stool, oversized me, and the idea that if I ever do need a walker or wheelchair to shower, the glass would have to come down - we have a shower curtain, not glass doors. With this configuration, I am very glad that I insisted on a floor drain in the room. The room floor is actually a sloped Kerdi shower system. Our ”trench” along the front edge of the shower pan is only about 1/2” deep. It came with a metal grate that I removed. There is a 4” square drain in the center, just behind the trench, covered in the solid surface material. Behind the trench, the shower pan manufacturer has fashioned a 1/2” high curb that is shaped like a triangle, to allow tires to climb it on the way in and out. They added this to direct the water to mostly go to the center 4” drain, making the shallow trench a back-up. The pan slopes to the front. It drains well, no standing water is left anywhere. I flooded the bathroom twice. The first time, I simply took a chance and did not check the 4” drain to pull out the hair. I go through a lot more shedding now that I am older, and my hair is long. That time, the floor got wet, but the floor drain handled it fine. The second time, I had a bath rug between the shower and the drain and the water flowed out into the hall. The rug had blocked the flow of water to the drain, redirecting it towared the door, and the slight slope of the shower kit under the floor tile did not overcome the water’s flow. I had water across the hall in the linen closet. So, now the bath rug remains to the side of the shower and I step onto often wet tiles with my hand gripping the vertical grab bar at the edge of the shower, before reaching the dry rug. It is easy to hit the curtain with the hand-held sprayer and get the floor wet. The floor drain does its job and the wet floor is often dried by the radiant heater near the ceiling before I am done fussing with my hair. I would not recommend a curbless shower with a front trench drain without an additional floor drain outside of the shower. Yes, this makes it more expensive, but it is the only safe way to make a shower that is small and wheelchair accessible. My shower pan is 37 3/4” deep and 63” wide. We live in a ranch style home over a basement, and lowering the subfloor by putting it between the floor joists and level with the top of the joists was all we needed to do to make the shower pan level with the room floor with the shower sloping kit and Kerdi under the room floor tile. We do have a bit of a rise up from the hallway to enter the bathroom from the hall, to get the height needed for the Kerdi kit to slope the floor for the floor drain. It has not tripped up anyone yet, and I try to remember to warn folks about it. Ideally, a wheelchair shower would have three walls around the showering area, with the end open to wheel the chair in., with a drain opposite the door end. One side wall could be a low pony wall, to allow a caregiver to reach in and assist. There are also ”caregiver doors” that are short, bifold glass doors. You install a shower curtain above them. The doors keep the aide fairly dry, I would guess. It would keep the water in the shower, too.