Figured it out:
I added a hook to the android platform in config.xml
<hook type="before_prepare" src="scripts/020_copy_resources.js" />
In the hook, I ran a script based on this answer, saved in <project>/scripts/020_copy_resources.js"
#!/usr/bin/env node
// Native resources to copy
var androidNativePath = 'native/android/';
// Android platform resource path
var androidResPath = 'platforms/android/res/';
// Copy native resources
var rootdir = process.argv[2];
var fs = require('fs');
var path = require('path');
function copyFileSync( source, target ) {
    var targetFile = target;
    //if target is a directory a new file with the same name will be created
    if ( fs.existsSync( target ) ) {
        if ( fs.lstatSync( target ).isDirectory() ) {
            targetFile = path.join( target, path.basename( source ) );
        }
    }
    process.stdout.write('Copying ' + source + ' to ' + targetFile);
    fs.writeFileSync(targetFile, fs.readFileSync(source));
}
function copyFolderRecursiveSync( source, target ) {
    var files = [];
    //check if folder needs to be created or integrated
    //var targetFolder = path.join( target, path.basename( source ) );
    var targetFolder = target;
    if ( !fs.existsSync( targetFolder ) ) {
        fs.mkdirSync( targetFolder );
        process.stdout.write('fs.mkdirSync( ' + targetFolder + ' )');
    }
    //copy
    if ( fs.lstatSync( source ).isDirectory() ) {
        files = fs.readdirSync( source );
        files.forEach( function ( file ) {
            var curSource = path.join( source, file );
            if ( fs.lstatSync( curSource ).isDirectory() ) {
                var newTarget = path.join( targetFolder, path.basename( curSource ) );
                copyFolderRecursiveSync( curSource, newTarget );
                process.stdout.write('copyFolderRecursiveSync(' + curSource + ', ' + newTarget + ' )');
            } else {
                copyFileSync( curSource, targetFolder );
                process.stdout.write('copyFileSync(' + curSource + ', ' + targetFolder + ' )');
            }
        } );
    }
}
if (rootdir) {
    copyFolderRecursiveSync(androidNativePath, androidResPath);
    process.stdout.write('Copied android native resources');
}
This copies any files/folders in <project>/native/android to <project>/platforms/android/res
I then followed this answer to build the theme for the date picker. For my purposes, I only needed to set the colorAccent and colorBackground in the main theme and the datePickerDialogTheme.