Hi Colecg and welcome to our forum,
I'm going to ignore the fact that your solution seems overly fragmented and hard to maintain and just respond to your question ....
Note: I'm assuming you are not using content types. Content Types could help you simplify the maintenance of your form templates (XSN) since publish once could update all libraries. But, we'll assume you are not using these since your architecture is really bad as it is.
Fastest solution would be to install the free QRules v2.3 trial and use the command which allows you to submit a form XML to a different SharePoint library/site. Works with rich client forms but not browser. That's the fastest and probably cheapest way to go but it does require purchasing a cheap product later ($200).
Of course, if you are using rich client, you can just use Save As too but that won't update the href to point to the new template. To manually update the href you can file->save the form XML to your local computer's desktop, open that XML in notepad and change the href in the XML to point to the new site. Save the XML back. Double click it to open in InfoPath rich client and then submit. Only works in rich client. No browser support.
You could change your form to add a rule that launches a new InfoPath form and give it the location of the target form library. However, this won't copy the values in. Assuming the schemas are the same, you could use File->Merge Forms from the target to pull the source form's XML. That might be an easy solution with no cost.
You could also add a button to your form that launches the target form template with input parameters. The input parameter is the location of your source XML. When the target XSN opens it can load the source XML into the form and copy the values. Requires qRules and a little extra code, but doable. Unlike the first approach this can be done in the browser but would require admin deploy since the form would have code.
You could open the target and have it pull data from the source form in. Assuming that your InfoPath form libraries have the fields promoted so they show up as columns in the library, you can just copy those values into your form using rules and a SharePoint URL data connection. Easy to do but the data connection would be hard-coded so you have to specify it. You could add code to do this on demand based on some value in the form but that would be more work.
Hopefully one of these ideas seems interesting to you.
Happy trails!