I think the oft-cited EBT restriction that prevents it being used to pay for something online, and requires it at the "actual time and place" of the sale, is a paraphrase of 7 CFR 2.274.7(b).
(b) Prior payment prohibition. Program benefits shall not be used to pay for any eligible food purchased prior to the time at which an EBT card is presented to authorized retailers or meal services. Neither shall benefits be used to pay for any eligible food in advance of the receipt of food, except when prior payment is for food purchased from a nonprofit cooperative food purchasing venture.
So normally you can't. But those constraints may be going away soon: The Agricultural Act of 2014 a few years back added subsection 7 USC 2016(k) to the SNAP statute, mandating enabling "On-line Transactions" (under the heading of Technology modernization for retail food stores):
(Sec. 4011) Requires pilot projects, which shall be completed by July 1, 2016, to test the feasibility of allowing qualifying retailers to accept SNAP benefits through mobile transactions and on-line transactions.
Requires the Secretary, by January 1, 2017, to: (1) authorize implementation of such projects in all states unless the Secretary makes a finding that implementation is not in the best interest of SNAP, and (2) report to Congress regarding the basis for any finding to not authorize.
Reading the old thread about this, I noticed FreshDirect's convoluted EBT-on-delivery program (which no online retailer would normally want to imitate) goes as far back as 2012, so it's of no relation to this 2014 law. It was just struggling under the original regulations, it's not a pilot project.
So I don't know how many of these USDA "demonstration projects" have run or where they even have, or how hard it would be in practice to apply to become one with just 4 months remaining now. (Or if that was what Rob meant on Reddit about "Government is slow" or @Conor meant by 'looking into it', actually.) But even without that, by year's end it looks like real online EBT ordering might be more of a reality if the USDA actually listens to Congress?