jyl, my approach is just like yours and there is something to it. It goes back to my pre-teen years when I had a Raleigh Sports 3 speed. The shift cable broke leaving only 3rd gear, so I rode that way about a year.
When I finally put on a new cable, found I was a much stronger rider. This was also the time I had a growth spurt and left childhood asthma problems behind so that helped too, but grinding uphill in high gear and running were my main exercises and suddenly I had muscles!
The growth in strength was quite impressive for someone who was always the smallest/weakest. It was life changing to ride off or run ahead of all my friends. Don