I don't know why TurboTax is not letting you e-file, but filing an amended return by mail does not make a significant difference in the IRS processing time. All amended returns take 20 weeks or more to be processed, no matter how they are filed. The minor advantages of e-filing an amended return might not be worth the time and effort it would take to resolve the problem. Mail the return by certified mail with a return receipt so you at least have proof of delivery. It's rare for the IRS to actually lose a return.
You can check the status of your amended return using Where’s My Amended Return? on the IRS web site. You can check the status about 3 weeks after you file it, either e-filed or by mail.
