I imagine the entire ordeal might not be doable due to how long it would take and phone lines cannot really compete with the internet as a mode of signal transfer for something as complex as mining?
I do think mining over a 56 Kbps modem might be possible. I have technical experience writing code with the Stratum protocol. First of all, the machines would need to be connected to a local Stratum proxy. The proxy will need to set a high enough share difficulty to minimize back-and-forth communication with the pool. Since BTC has long block times, there should be no problem broadcasting the jobs over 56 Kbps or even 10 Kbps. Even if the latency is 1 second, that will only result in a stale rate of 0.17%. Even for coins with fast block times like ETH, dialup could work.
But I would turn to tall 4G antenna or even a 3G modem first. Worst case, IPv4 over ham radio.