Ie the 60degree threaded plates fit the 55 degree spindle nose
Draw a picture of a theoretically exact male Whitworth form thread.
Draw a picture of a theoreticaly exact female UN form thread.
Overlay the two and appreciate the issue at a theoretically exact level.
Adjust one or both* until there is no interference and an amount of clearance that looks right to you.
Assess whether the new dimensions fit within one of the standard thread classes for that thread form.
Whitworth and UN can be made to interchange if the tolerances are large enough. Commercial nuts and bolts do so by observation, so their tolerance is an upper limit to this calculation. Your calculation above would give the lower limit to this.
* Measuring your spindle with proper thread wires to determine its actual pitch diameter would give a reference for your own situation.