So 4,600 nm with a full load, against the winter polar jet stream, is getting close to the operational effective range.
For the 763ER the official still air, sea level, passenger only range is 5990 NM.
Boeing: Commercial Airplanes - 767-300ER Technical Characteristics
A real world reduction of ~25%. For a rewinged A321/A322 a "brochure" range of ~5000- 5300NM would be required to make it an effective medium range platform..
From e.g. London such an A322 could efficiently cover Europe, the US East coast, northern Africa, the Middle East and some more if you start pushing it.
4000NM & 5000NM ranges
From ATL (big 757/767 base) it would cover the US unrestricted, Hawaii, Western Europe, the Caribbean and Brazil.
4000NM & 5000NM ranges, ETOPS180
A suitable engine could be the Pratt & Whitney developed new GTF engine, able to handle up to 40,000 lbs, a 20% bump over the current max power availabe for the A321. That should be sufficient for a bigger medium range A322's MTOW.
GTF able to power twin-aisle narrowbody: Pratt & Whitney