Never received any responses, but that's okay. I have since figured the problem out.
While I thought the only drivers were contained in the self-executing file upon the device itself, that was not the case. When it installed, unbeknown to me, it installed a "\program files\Novatel Wireless Modem\Drivers" folder.
Now on other laptops, it went ahead and installed the correct devices for all items and I never even knew of the folder. For whatever reason, on this particular laptop I have, it did not install completely. But, once I found that folder, it was a simple matter of going into Device Manager, clicking on "update driver" on each of the "Data Interface" listings under Other Devices, and pointing it to search in the Novatel driver folder.
After that, it was smooth sailing and everything worked as it should.