From the limited teaching we had on the SR-71 on the hard sums coarse I know that a suitably light SR71 that was somehow / actually in the best bit of the CofG envelope, with sufficient LN2 density, operating at a lower altitude that also happened to be unusually cold, with intakes in fully automatic (and trusting that they would remain so(!)) at a reduced mach number (say M3.0 or below), in a flight regime that allowed up to 25º AoB whilst remaining within the limited AoA range etc, then you could probably achieve a turning radius of under 100nm. Easy.
None of what you postulate is relevant I’m afraid, see graph.
Centre of Gravity limitations were numerous, but basically,
Take Off – Forward of 22% MAC
Subsonic – 17 to 22%
Supersonic below 3.2M – aft limit 25% (desired position as there is a 50 nm loss of range per % CoG forward of 25%). Fuel transfer used to keep it there.
I recall that real-world ops tended to have few, if any, of the favourable conditions above and with an AoB limits reducing towards zero makes turning at operational altitudes / mach a serious challenge. I do recall (with reasonable certainty) that any manual control of the intakes (as an example) at typical operational altitudes had a 0º AoB limit. Tricky.
Manual control of intakes imposed no flight restrictions, though did impose cautions. The only non turning flight limitation on high altitude turns was for flight at or above the Maximum Altitude Cruise Profile for the existing Mach, gross weight and ambient temperature, a 35° angle of bank at this altitude the angle of attack would exceed the 8° supersonic limit. A 2,000 ft descent prior to turn entry was recommended ie to the Intermediate Altitude Cruise Profile.