Comment by Animats

As mentioned, that had a tough sync problem. SIGSALY changed its key every 50ms. The mechanical synching of two turntables within that range was possible. That worked because the audio was being compressed pretty hard before encryption. Delilah, which works by using a modular analog adder to add signal and key noise, would need a new analog key value for every audio sample. Probably 3KHz or so, or about 300usec. That's beyond the precision of sync which can be achieved reliably by mechanical means.

A little bit of analog buffer would help. It wouldn't be a problem for transistor era electronics. You need something like an analog shift register (see "bucket-brigade device"[1]) Those were not developed until the 1970s, and, for a while, appeared in guitar pedals, reverbs, and other simple audio processing devices. If you had to do that with tubes, you'd have a whole rack of tube delay line.

Fun retro electronics project for someone.

[1] https://en.wikipedia.org/wiki/Bucket-brigade_device