Are there any software-based solutions that don't involve physical intervention for a P07 error?

The primary software-based solution is using a service tool to reset the waste ink pad counter. If the error is due to a faulty sensor or a minor glitch, a full printer reset (often by unplugging the power for an extended period) might sometimes clear temporary errors, but it's unlikely to resolve a P07 error if the pad is genuinely saturated or the counter needs a manual reset.