Proper way to pre-fill a sender's signature in bulk?

I currently have a working DocuSign integration going using embedded signing. An administrator logs in, provides consent once (auth code grant, extended scope) and the app can generate sign requests in their name to different users without them needing their own DocuSign accounts.

What I'm trying to build now though is for the administrator to sign as well, and preferably only once for the same document which is then sent to different users. So I'd like to make an embedded signing view for the admin to sign once, then use this same half-signed document/template to create multiple embedded signing views for different users. My client would like the DocuSign audit trail to show that the administrator signed each document, so just pre-filling it with an image won't do.

I've been looking at templates, but haven't been able to find examples of or methods for including a sender signature in a template, or embedded template editing. I'm using the eSign package for C# by the way.

So my question is, is this even possible, and if so what's the proper way to achieve it?