Hi Noah,
Not that I've found using Postman as it only return a single handle for the upload and not an array 😣 which would be easier to parse.
I had to build a mac desktop application which does exactly this for our company which uploads multiple files, moves files to associated Project/Tasks, adds user time to the task and can attach a custom form to the document, this might be the better way to go if your able to do it or you can do it if you have Workfront Fusion.
If you need to get the handle of the upload in Postman you can use the following, put it under the Tests tab, create an environment variable called handle.
var jsonData = JSON.parse(responseBody);
postman.setEnvironmentVariable("handle", jsonData.data.handle);
I only use Postman for development so I can get my code calls right.
Sorry I couldn't be any more help for you.