Howdy Jaybird
One other thing you might need to do, Do you run regular or lowish profile tyres?
If the latter you may need smaller inner tubes. When I completed the restoration of my CGT I had new tyres fitted all round and within a year I had had a flat in all 4 tyres, the first within a month of getting the car on the road.
It turns out that 15" inner tubes (MGCs have 15" wheels not 14" like MGBs)are too big to fit modern 15" tyres, the result when fitted? a crimp in the inner tube which eventually becomes a weak spot and fails. Might need to use smaller inner tube for the B's as well.
If you can't ger rim straps then an old inner tube can work.
Like the others I'm amazed that any of your tyres held air at all without tubes, the inner ends of teh spokes are designed to flex in their holes so there is no way they can be air tight.
best regards
Tom