Thanks to these answers by @Günter Zöchbauer:
...I have pieced together an approach like this:
index.html
<!DOCTYPE html>
<html lang="en-us">
<head>
    <base href="/" />
    <meta charset="utf-8" />
    <title>Testing APP_BASE_HREF</title>
    <link rel="icon" type="image/png" href="favicon.ico" sizes="16x16" />
    <meta name="viewport" content="width=device-width, initial-scale=1" />
</head>
<body>
        <app-root></app-root>
</body>
</html>
app.module.ts
import { APP_BASE_HREF, PlatformLocation } from "@angular/common";
import { AppComponent } from "./app.component";
/**
 * This function is used internal to get a string instance of the `<base href="" />` value from `index.html`.
 * This is an exported function, instead of a private function or inline lambda, to prevent this error:
 *
 * `Error encountered resolving symbol values statically.`
 * `Function calls are not supported.`
 * `Consider replacing the function or lambda with a reference to an exported function.`
 *
 * @param platformLocation an Angular service used to interact with a browser's URL
 * @return a string instance of the `<base href="" />` value from `index.html`
 */
export function getBaseHref(platformLocation: PlatformLocation): string {
    return platformLocation.getBaseHrefFromDOM();
}
@NgModule({
    declarations: [
        AppComponent
    ],
    providers: [
        {
            provide: APP_BASE_HREF,
            useFactory: getBaseHref,
            deps: [PlatformLocation]
        }
    ],
    bootstrap: [
        AppComponent
    ]
})
export class AppModule { }
app.component.ts
import { Component, OnInit, Inject } from "@angular/core";
import { APP_BASE_HREF } from "@angular/common";
@Component({
    selector: "app-root",
    templateUrl: "./app.component.html",
    styleUrls: ["./app.component.scss"]
})
export class AppComponent implements OnInit {
    constructor(@Inject(APP_BASE_HREF) private baseHref: string) {
        console.log(`APP_BASE_HREF is ${this.baseHref}`);
    }
    ngOnInit(): void {
    }
}
app.component.spec.ts
import { TestBed, ComponentFixture, async } from "@angular/core/testing";
import { APP_BASE_HREF } from "@angular/common";
describe("AppComponent", () => {
    let component: AppComponent,
        fixture: ComponentFixture<AppComponent>;
    // configuring dependencies
    beforeEach(async(() => {
        TestBed.configureTestingModule({
            declarations: [
                AppComponent
            ],
            providers: [
                {
                    provide: APP_BASE_HREF,
                    useValue: "/"
                }
            ]
        }).compileComponents();
    }));
    // getting component
    beforeEach(() => {
        fixture = TestBed.createComponent(AppComponent);
        component = fixture.componentInstance;
        fixture.detectChanges();
    });
    // tests
    it("should create the app", async(() => {
        const app: any = fixture.debugElement.componentInstance;
        expect(app).toBeTruthy();
    }));
});
Then you could do stuff like this:
- npm start
APP_BASE_HREF will equal the default value set in index.html
- npm run build --base-href /foobar/
APP_BASE_HREF will equal the value passed to the base-href flag