I think what you did is fine. A slight improvement would be to find the combination of shims that get the headstock parallel to the bed in both the horizontal and vertical plane with the bed level.
For the test you did with the backplate, if I understand correctly, you moved the cross slide so the indicator hit the bolt at the front and back? This is the test that is normally done to confirm that the cross travel is perpendicular to the bed after you know the head is aligned. It is testing both things.
I am in the process of rebuilding a 10L lathe. The bed was worn so I had it planned then I scraped the ways flat. Next step was checking alignment of the head stock to the bed. It was way off. I used a test bar with the bed perfectly level. The test bar results are
not impacted by cutting force. Plus its quicker to run an indicator along the top and side of the test bar then set up a cut. Next was a process of scraping the bottom of the headstock until it was in alignment to the bed. It took many iterations but finally got there. I did some tests along the way with shims, exactly like you did, just to verify where I needed to scrape on the headstock.
Next the the tailstock was scraped in for alignment to the bed and height of the headstock.
Hard to say how your lathe got in the condition it was in, perhaps a quality escape from the factory or something happened over the years.