I would bring your electronics into the 21st century ASAP. We upgraded our 30A to 40 A and had our new cooktop installed all in the same day. In fact, we created a new subpanel in the basement stairway right off the kitchen so I can cut power in an emergency without running downstairs to the basement main panel. Just mentioning this because maybe installing a new subpanel for your new range is faster/less complicated than you think. Expensive, but infrastructure is worth the investment.

Is that a Crouse-Hinds breaker box? Having upgraded in the late '60s to one (Sears brand) from the original 1955 Edison fuse box, and further upgraded and added boxes over many years, I can relate that Siemens is the present manufacturer of Crouse-Hinds style breakers. There are also Internet sites that sell "repurposed" elderly breakers.

(Also, for full disclosure, the generic use of 8 AWG for 40A circuits has some caveats depending on various details, including the 80% rule, so your case may or may not conform. I'm sure it will temporarily be OK with partial burner operation, but as you may appreciate, this is not considered a solution due to not being controlled by the hardware, but only by human informed intent.)

Our first home, bought in 2007, was from 1958. The only thing the house inspector told us that was useful was to get our breaker box updated. He said they were known to catch fire and best to switch it before we had any problems. I can't remember the brand but you may want to google yours and check.