If it's that close to the deadline don't you just sent them off with a paper filed return and a Flat rate envelope with tracking on it? That only leaves you one day to file.
I just use Paypal SHIP NOW, (paypal doesn't really advertise this as a feature, but it's awesome). I just print the label and tape it to the envelope, the taxpayer signs and seals it himself, and drops it off in the mail.
Tracking, shipping, everything is done in one shot and it costs $4.50. I just tack my time onto the bill, it takes only 5 minutes to do the label. YOu get online tracking, too, so you know when the return is delivered.
I print a PDF copy (of the label) for myself, too, so I have the taxpayer's proof of mailing. One tip, though, it says "First name" and "last name" when you fill out the label on Payal, so to ship to the IRS, I do "DEPT of" and then the last name "The TReasury).
https://www.paypal.com/us/cgi-bin/webscr?cmd=_ship-nowDealing with an e-file rejection after the filing deadline has been a nightmare for me in the past, even though I followed all the directions for submitted a return during the "10 Day Transmission Perfection Period" (yes, that's really what it's called).
Save yourself a headache.