I'm not sure if this is the best or only way to do it, but I followed this doc (https://www.amcharts.com/docs/v4/tutorials/creating-custom-maps/) and was able to figure out a solution.
I downloaded a GeoJSON file of the USA, opened it in mapshaper.org to make a few tweaks to the shapes, and then saved it in a .JS file like that doc directs.
Then, I used the worldLow orthographic projection with my custom map overlaid as a MapPolygonSeries.
// Create map instance
let chart = am4core.create("chartdiv", am4maps.MapChart);
// Set base map (worldLow)
chart.geodata = am4geodata_worldLow;
chart.projection = new am4maps.projections.Orthographic();
let worldSeries = chart.series.push(new am4maps.MapPolygonSeries());
worldSeries.useGeodata = true;
// Overlay series (Custom USA with states)
let usaSeries = chart.series.push(new am4maps.MapPolygonSeries());
usaSeries.geodata = am4geodata_worldUSA; // Your custom dataset