IIRC the fuel leaks on the ground were because the sheet metal was all fit rather loosely to allow for expansion in flight. At the speeds it would fly, the skin got quite hot.
But it is the fuselage gaps which was leaking, not the engines. After the elastomer filler broke down due to heat cycling. They needed the elastomer because the fuselage was heating up during flight which made it expand.
I'm sure we could "fix" it. But changing the engines doesn't seem to be the right way to achieve that.
You'd probably be using some mix of better turbofan/turbojet engines along with ramjets/scramjets and 50-60 years of materials sciences advances. So, yes.
Don't underestimate the J-58. This is as much if an extraordinary engineering feat as the SR itself.
I respect the J58's place in history, but it has no place in modern aviation. The ideas behind it still remain relevant, but the implementation is long, long outdated. I think it could be redesigned and reimplemented for cheaper that it would cost to resurrect and maintain the original J58.