Help calling an add-on method via AJAX

I’m working on updating a fieldtype add-on to work with EE3. This add-on calls one of its own php functions from a javascript file to make some DB updates without reloading the page.

In EE2, the javascript called the function using $.get and a URL formatted like this:

http://www.mysite.com/admin.php?S=0&D=cp&S=0&C=addons_modules&M=show_module_cp&module=module_name&method=method_name&param1=param1value&param2=param2value

This style of URL is not working for me in EE3 - I am getting a 404 not found error in the console when the $.get runs.

What format do I need to use for the URL in EE3 to access a function of my module (and pass in parameters)?

I thought I might be able to use an ACT to accomplish this, but I need the module to work on multiple installations so I can’t hardcode the ACT id into my javascript file (and I’m not aware of any way to pull the ACT id from the database in a javascript file).

I really appreciate your help!