
Here is the link to the classic Mini open ended wheel nuts I am now using.
https://www.ebay.co.uk/itm/304564911790 ... R87Rv6r0ZQ
From the dimensions you have given you should have had enough thread for the capped nut to hold the wheel without bottoming out.
You do not need to utilise all of the thread on the studs to secure the wheel just threads of at least twice as long as the stud diameter.
So I suggest two possible theory's for the wheel loss:-
1. The wheel nuts were not tightened to the 38lbf ft torque as specified in the Minor workshop manual.
2. The wheel nuts were over tightened which lead to the studs snapping.
What ever the cause you survived the incident and that is the most important thing.
As an aside - I would check that the wheel centre inner face sits square and fully on the brake drum outer face without any fouling of the raised face of the half-shaft.
Phil