You can get ready to roll (wire) tuners and amp boards on eBay (direct from China) for cheap, single-digit $. They would easily fit in a 9x9x3 area. Trying to get the vintage case mechanical tuner dial and needle pointing to the number that corresponds to the actual tuner frequency, THAT would be more challenging, might have to involve brackets and gears to get all sorted out, or you'd just lose that aspect of vintage and instead of an analog needle range, there's an LCD display in its place, though a tuner with a display might exceed my claim of single-digit $ cost.
Another option is hack the circuit. It's set to a particular gain, which could be adjusted down till it's far closer to 1VAC. Reverse engineering something from that era would give me a headache, but so would what you want to do instead.
Keep in mind that electrolytic capacitors don't last forever. If you want this to have a decent tour of duty then you may want to replace many if not all of those.