If a large horizontal loop antenna, insulated but laying at ground level, works as an MF and low HF receive antenna, why (even though it has very high ground losses) can't it be used for transmit (to the stations it can hear) via the reciprocity theorem?
You can transmit, and it might work.
One of the magic things about HF is that the path loss is often so low, because of the reflection from the ionophere, that even terrible antennas work OK. You'll find tons of stories of people working the whole of europe with a loop of wire around their desk, or a coathanger, or something.
This is not to answer directly, but to warn about applying reciprocity.
While it's true that (passive) antennas transmit and receive with the same efficiency, and same radiation pattern, you also need to consider the effects of external noise.
Receiving: At the bottom of HF, and MW, a receiver is very much externally noise limited, which means that the signal fades into the noise not because the receive antenna is too small, but because the background noise is too strong. Because the noise (and the signal) are so strong, the receive antenna can be made very, very small before it starts to matter how poor it is. For example, in typical conditions, a little transistor radio is externally noise limited, with its 1 m whip or 20 cm loopstick for MW. The key thing to remember is that within reason, the signal sounds the same, whether the receive antenna is small and inefficient, or full size.
When transmitting, things are very different. A full-length dipole will have at least 20 dB more gain than a little 1 m whip, which means the radiated power is 100 times larger. This makes the signal strength at any receiver 100 times better, and hence the signal-to-noise ratio, and the quality of the signal. So the key thing here is that when transmitting, every dB of gain results in a stronger-sounding signal.
For any given Tx-Rx path, there will be a minimum ERP which will make the transmitted signal stronger than the noise, as seen at the receiver. Drop below this and you won't be heard by that station. If the other guy is transmitting with a full-size dipole, you might hear them with any antenna, but you'll only overcome the noise if you also transmit with an antenna of similar efficiency.
Ground losses introduce additional attenuation in the path between the stations. Reciprocity applies, but this additional attenuation is more of a practical problem for transmitting than it is receiving.
Say the ground losses amount to an additional 20 dB of attenuation. To offset this additional loss, you can add a 20 dB amplifier.
For receiving, you'll need to handle powers on the order of microwatts or even less. Any transistor can handle this power, so components are cheap.
Overcoming antenna inefficiency with additional gain in the receiver is feasible as long as the amplifier's noise floor is significantly below the RF noise floor. In practice this is trivially accomplished for HF and lower frequencies because the RF noise floor is so high. See How can I calculate the effects of an LNA, antenna gain, etc. on noise performance?
For transmitting, you'll probably want much more power. If you want the radiated performance of a 100 W station with an efficient antenna, you'll need an amplifier capable of 70 dBm or 10,000 W. This is not a cheap proposition.