You should probably start by making a config variable for the API URL. Check out how MobileFrontend does it (https://git.wikimedia.org/blob/mediawiki%2Fextensions%2FMobileFrontend.git/a4372c2b5402db3d406f176d4235d726d5cc9d99/MobileFrontend.php#L163).

You can export that to JavaScript with https://www.mediawiki.org/wiki/Manual:Hooks/ResourceLoaderGetConfigVars .

Then, pass that to the UploadWizard config.

However, you will need to deal with CORS (https://developer.mozilla.org/en-US/docs/HTTP/Access_control_CORS). In the past, such cross-domain AJAX requests never worked. Now, they can, but only if CORS is configured. You will need to change UploadWizard to deal with this, since it does the actual uploading.

MobileFrontend shows how to handle CORS as well (look at PhotoApi.js).

However, you will not be able to change the production (actual Wikimedia Commons) CORS config to allow access from http://pronunciationrecording.instance-proxy.wmflabs.org/

You might be able to get permission to test against https://commons.wikimedia.beta.wmflabs.org/w/api.php (Beta Commons) (ccing Antoine for this). Otherwise, you'll need to set up your own destination wiki to test with (separate from http://pronunciationrecording.instance-proxy.wmflabs.org/).

For reference, the Beta config for CORS is at https://git.wikimedia.org/blob/operations%2Fmediawiki-config/3a9cdd74eefd74b3224af540c1abf419c5a71c44/wmf-config%2FCommonSettings-labs.php#L106

I think a lot of what you need here is now abstracted away in mw.Upload.