Any amended return takes ages to be processed, a minimum of 4 months and often longer, no matter how it's filed. The only difference between e-filing and filing by mail is the few days that it takes to get to the IRS.
Right now all IRS e-fling is shut down to prepare for filing 2024 tax returns. Nothing can be e-filed until the IRS reopens e-filing, which will be sometime in January. They have not yet announced a date. So it will actually be faster to mail your amended return now than to wait until e-filing reopens in January. But again, processing of any amended return is going to take a minimum of 4 months, and possibly longer.
