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Ermi has addressed your major question in his reply and I just wanted to add this for clarification:
You wrote “But AM bandwidth is 10KHz, which isn’t very wide, and exceeding this would be a violation.“. Part 15 rules for AM do not restrict the bandwidth used providing out of band emissions are attenuated per the rules. Obviously, using wide bandwidth on the AM band increases the chances of interference with licensed stations which would be prohibited (and rather unwise) but there is no bandwidth restriction per se other than this practical constraint. Damped waves (such as from spark gap transmitters) are not permitted.
Minor point but I thought you would be interested.