My current favorite bike is a 1995 Litespeed Ultimate with a Time carbon fork and R8000 Ultegra kit. I don't know if Titanium is "magical". I just know that, out of 9 bikes that I have to choose from, the first one I'd grab would be the Litespeed. Between the frame and fork, the groupset, and the other ancillary bits to make it into a bike, it was probably just about within your price range.
Note - bought the frame and fork as a complete bike, possibly for cheaper than if I'd just bought the frame, because the other components were all worn out and the whole thing looked like crap. But under all that, the frame and fork were in great condition.
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"Don't take life so serious-it ain't nohow permanent."
"Everybody's gotta be somewhere." - Eccles