The Rules from Part 15 paragraph 15.221 apply (see below).
An average AM broadcast receiver would have to be located very close to the power line in order to receive a useful signal from a legal (compliant) carrier current system.
The 15 uV/m field given in 15.221(a) is below the noise level in most receiving locations outside of a shielded room, and for an operating frequency of 1600 kHz the distance to that legal field intensity from a carrier current system is about 100 feet. An average receiver probably would need to be located within 25 feet of the power line in order to receive a fairly noise-free signal (assuming the 60 Hz power line hum was controlled).
Sorry that this situation probably is not very good news, but it is based on FCC and physical realities.
RF
____________
§ 15.221 Operation in the band 525–1705 kHz.
(a) Carrier current systems and transmitters employing a leaky coaxial cable as the radiating antenna may operate in the band 525–1705 kHz provided the field strength levels of the radiated emissions do not exceed 15 uV/m, as measured at a distance of 47,715/(frequency in kHz) meters (equivalent to Lambda/2Pi) from the electric power line or the coaxial cable, respectively. The field strength levels of emissions outside this band shall not exceed the general radiated emission limits in §15.209.
(b) As an alternative to the provisions in paragraph (a) of this section, intentional radiators used for the operation of an AM broadcast station on a college or university campus or on the campus of any other education institution may comply with the following:
(1) On the campus, the field strength of emissions appearing outside of this frequency band shall not exceed the general radiated emission limits shown in §15.209 as measured from the radiating source. There is no limit on the field strength of emissions appearing within this frequency band, except that the provisions of §15.5 continue to comply.
(2) At the perimeter of the campus, the field strength of any emissions, including those within the frequency band 525–1705 kHz, shall not exceed the general radiated emission in §15.209.
(3) The conducted limits specified in §15.207 apply to the radio frequency voltage on the public utility power lines outside of the campus. Due to the large number of radio frequency devices which may be used on the campus, contributing to the conducted emissions, as an alternative to measuring conducted emissions outside of the campus, it is acceptable to demonstrate compliance with this provision by measuring each individual intentional radiator employed in the system at the point where it connects to the AC power lines.
(c) A grant of equipment authorization is not required for intentional radiators operated under the provisions of this section. In lieu thereof, the intentional radiator shall be verified for compliance with the regulations in accordance with subpart J of part 2 of this chapter. This data shall be kept on file at the location of the studio, office or control room associated with the transmitting equipment. In some cases, this may correspond to the location of the transmitting equipment.
(d) For the band 535–1705 kHz, the frequency of operation shall be chosen such that operation is not within the protected field strength contours of licensed AM stations.