[taildragger]

You know those J58's have a horrendous TSFC. Their are many Turbofan's with approx the same 4000 lbs of thrust per unit. An upgrade to a modern Biz-Jet Turbofan would do wonders to range. I don't have time to do a rough calc, but maybe some other arm-chair aero-FR-enganear can :-). BTW love these birds...

[TalonDJ]

You would have to retro fit of burner or give up on breaking Mach.
I did an internship with an outfit making electronic engine controls in the late 90s. They still had a line open building some some positively ancient looking circuits. They were for folks still flying J58s that needed the same old vintage 50’s gear, but newbuilt replacement parts. Certainly falls under the ‘if it ani’t broke’ clause in engineering.