FWIW Origin 8 sells an ISO cartridge BB in 115 for like $35. (it wouldn't surprise me if all the Taiwan sourced cartridge bottom brackets are made in the same factory)
I think there's a reasonably good chance it will work with your Avocet crankset. Going from JIS to ISO will bring in your crankarms about 4-5mm on each side, depending on who you ask. That should get you fairly close to ideal for fit on the spindle/crank interface. Should be reasonable for chainstay clearance also.
Did you measure you chainline as it stands now? It's a little tricky to do but it would be helpful.
https://www.sheldonbrown.com/chainline.html