I’ve seen this exact thing done for an event, but I don’t have the code for it. They had a JS application that you could type your name into and it would resize the text to fit in the label size.
If you want to do this within Inkscape, I’d suggest to make a template document the size of the paper, have the guests type within a text box there, and then use AxiDraw Merge to plot it — It will automatically replace the text with a stroke font and plot it.
Once you’ve done the first one, you can use Extensions > Previous Extension (or alt-q) to print the next one. So, just type and then a single keystroke to do text substitution and print.
Alternately, there are ways to do text substitution and drive the AxiDraw from the command line, but they aren’t as well integrated.