Your questions, " I need to configure an HTTPS monitor to use the PUT method instead of the GET method. Is there a way to do that in ASM?"
Here is a response that I got from one of the l2 engineers.
the HTTP/S monitor types in ASM only support GET and POST. There's a new agent coming that might support additional methods but that's a long way to go at this point.
The easiest way to customize their HTTP(S) requests in any aspect is using a JMeter script to do that.