Despite them being complex, high-bypass turbofan engines ARE exotic technology. There are vanishingly few countries/companies that have the expertise necessary to produce the single crystal fan blades used in the engines of these aircraft.

As far as the SR-71, its engines were turbojets that transitioned to ramjets above Mach 2ish. They required a special grade of jet fuel and a dedicated fleet of refueling aircraft.

I rather doubt an SR-71 successor would use a turbofan. The mission profile really doesn't require it. I would expect it to be a turbojet that transitions (as you said) to a ramjet and eventually a scramjet.

I would love to see the SR-71 fly again, if only from a nostalgia standpoint, but I really doubt this effort will be successful. I doubt even more that much of value can be accomplished by getting one to be flyable again that couldn't be achieved in a much more cost-effective manner via unmanned aircraft.