Reddit reviews Blum Soft-Close 110° BLUMotion Clip Top Inset Hinges for Frameless Cabinets

I'm not clear why you think regular inset hinges won't work. From the look of your picture, that's what you have.

> their kitchen cabinets at least are overlay.

Isn't 95% of Ikea overlay? If I understand overlay correctly, the door is stopped when closing (and rests) upon the frame of the cabinet. Billy, Besta, Alsvik.

Following your links above, I found 2 products using that hinge:

1. NORNÄS instructions that show an insert door. A photo of the NORNÄS Wardrobe confirms it was inset, but I've never seen this product and it doesn't appear on the website (it was an eco-friendly, solid wood design). Seems dead end.
   
   
2. BRUSALI Nightstand 502.501.57 that appears to be an inset door hinge, but it's a bit hard to tell from the photo. This appears readily available in the U.S., but the hinge isn't sold separately. I'm assuming you don't want to buy $50 of nightstand for every 2 hinges. Also seems dead end unless you can convince their parts department to give a shed-load.
   
   Assuming you haven't moved on yet -- I think you'd be better off just buying non-Ikea hinges from a hinge store and matching it with the Ikea parts. I mean a 2-second search found me these, which are $7 more than Besta hinges.

Did you make it using a face frame? Inset hinges I believe are the correct term you're looking for.
https://www.amazon.com/dp/B0036AYZ0M?_encoding=UTF8&%2AVersion%2A=1&%2Aentries%2A=0&showDetailTechData=1#technical-data

The link shows how they work with a face frame, this link would be for a frameless build.
https://www.amazon.com/Blum-Soft-Close-BLUMotion-Frameless-Cabinets/dp/B004K7V8UU/ref=sr_1_1?ie=UTF8&qid=1494730746&sr=8-1&keywords=BLUM+Top+Clip+Inset+Hinges%2C+frameless+cabinets

And this link would be for glass doors albeit for frameless style cabinet
https://www.amazon.com/Blum-75T4300-Cabinet-94-Degree-Function/dp/B0096UBIBU/ref=sr_1_1?ie=UTF8&qid=1494730856&sr=8-1&keywords=BLUM+Top+Clip+Inset+Hinges%2C+glass+doors

http://www.amazon.com/Blum-Soft-Close-BLUMotion-Inset-Hinges/dp/B004K7V8UU/ref=sr_1_1?ie=UTF8&qid=1397973310&sr=8-1&keywords=blum+frameless+hinges

SOSS hinges are garbage for all but the smallest doors. I'd need to see a pic to say for sure, but I believe these will work even on a curved application as you described. You need a 35mm Forster bit to install them