Since the Carter years (finally, something to thank Jimmy for) federal law has said that any document which required a signature, may be signed DIGITALLY and that has the full force of law. Now, finding software, especially free software, which will give you the ability to sign digital documents with a secure digital signature, that's a wee bit harder. But it is possible, the new Adobe on-line reader stuff is one of the options. Some of the electronic fax software also offers similar options, so the shop can send you a fax and you can digitally sign the return one. There are all sorts of options, mainly used in the real estate business where transactions need to happen "NOW" and be securely signed. Of course convincing your LDS to come into the 20th century (yes, just to the 20th) may be impossible.
But certainly if you could do something like have your wife do the O2 check while you skyped it to observe and confirm...or if you sent a signed email to confirm that you had just seen this and approved it...
The shop might have someone there who is able to think creatively and solve problems.
Or just ask them to mark the invoice "TANKS STOLEN." No release needed then, right?