I think you want to separate out what the program is telling you versus what the operating system is telling you.
The program does not know much of anything about printers. In the program, when you start to click on Print, all it knows is what the operating system is telling it about the availability of certain printers and what preferences there are for each one (e.g. paper size). If your local printer does not handle 11x17 paper, then it will never give you that choice. If you intend to get the map printed at a service bureau, then you need to contact the service bureau and get information from them about the printers they have.
Now, a completely different way to skin the cat is to export to disk. The map can be saved to disk as a JPEG file, or whatever. Then open the JPEG in Photoshop or similar graphics program. Then you can print it from within Photoshop. However, Photoshop is going to have the same limitations as to printers. It can only print to the print device that the operating system tells it about.
If you think that your local printer has the 11x17 capability, but somehow it is not showing up through the operating system, then you might ask that technical question to the printer company support crew. Maybe you need a newer printer driver or something.
I've had printers installed and working successfully, and then all of a sudden the operating system is telling me that there are NO printers installed. Often, simply restarting the machine will clear that kind of foolishness. That generally happens after a fault in the page printing routine, like trying to print something that does not allow printing.