You don't need two PCs. It's easier with a controller (select the option to keep the controller enabled even when XIV isn't the primary window), but:

Start in, say, a housing ward. Begin teleporting to Foundation.
The moment your teleport animation begins (the purple glow, not the actual portal/disappearance), kill the XIV process using Task Manager.
Log in on an alt, using the same computer, and Player Search should have what you need.