Well the issue is that QTP is single threaded. So presuming your script is already as efficient as possible the only way to reduce that would be to run it on multiple machines with multiple QTP licenses.
I would look at a different scripting language for this task and bypass QTP entirely.
QTP can definitely run for 26 hours, as long as the script is relatively stable. I've got some scripts that take 3-4 days to run. There can be some issues with memory if you're using Internet Explorer during the test run, so I'd recommend closing browsers every few iterations.
You can split the process if you can. I presume following steps can be done using QTP (create\export). Probably here you use QTP - Application combination to do this. The rest of the process(rename\copy to network off VM) can be done using VB Script or other scripts parallel.
"QTP has not been designed for Long Executions and if you want to run a test that will take a lot of iterations you need to release the QTP and AUT Memory in a dynamically way otherwise QTP could be very unstable."
I looked at the link. The main idea is to write a .vbs script that keeps opening QTP, running a script and closing QTP.
I would probably also include calls to kill QTP processes before restarting QTP/UFT.
Doesn't sound like a test to me, it sounds like a batch logging process and you should use an alternative solution instead of QTP.
If your ok with VBScript then go that way and investigate a solution with FileSystemObject handling. It will be much quicker. Then it will be down to how fast your system can process the create/export/copy etc.