I recently updated a 10 speed to 21 speed. (early 70's Suntour equipped Takara)
I used a triple crank from a donor bike and screwed on a 7 speed freewheel from another donor bike.
Previously, chain rings were 36-48 and the freewheel was a 14-28 (14-17-20-24-28).
Now, it's a 26-36-46 and a 14-28 (14-16-18-20-22-24-28).

I did need to use a new BB spindle that I got from loosescrews.com, since the old cottered crank type wouldn't work.

It sounds like my bike was equipped very similar to yours.