I don't see the He162 as a synonym for an 1-engined jet fighter
Germans will need to whip up something more docile, and perhaps using the other aircraft as part donors in order to speed up the production (besides the landing gear).
A problem is that the first generation "Class I" jet engines were maybe too weak to produce sufficient thrust for a single engine fighter that also carries sufficient guns, fuel, armor etc.? And the war is ending before Germany gets any of their Class II engines into service (HeS 011 etc.). Though if one insists on a single engine it should be possible to do better than the He 162 by integrating the engine into the fuselage. So maybe something like a slightly downsized Me P.1101 or Ta 183 with a HeS 30?